http://wiki.manchester.ac.uk/blocks/index.php?title=M(32,51,16)&feed=atom&action=history
M(32,51,16) - Revision history
2024-03-29T00:55:28Z
Revision history for this page on the wiki
MediaWiki 1.30.1
http://wiki.manchester.ac.uk/blocks/index.php?title=M(32,51,16)&diff=1026&oldid=prev
CesareGArdito: /* Covering blocks and covered blocks */
2019-12-08T16:16:51Z
<p><span dir="auto"><span class="autocomment">Covering blocks and covered blocks</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr style="vertical-align: top;" lang="en-GB">
<td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 16:16, 8 December 2019</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l37" >Line 37:</td>
<td colspan="2" class="diff-lineno">Line 37:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Let <math>N \triangleleft G</math> with prime <math>p'</math>-index and let <math>B</math> be a block of <math>\mathcal{O} G</math> covering a block <math>b</math> of <math>\mathcal{O} N</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Let <math>N \triangleleft G</math> with prime <math>p'</math>-index and let <math>B</math> be a block of <math>\mathcal{O} G</math> covering a block <math>b</math> of <math>\mathcal{O} N</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>If <math>b</math> is in M(32,51,16), then <math>B</math> is in M(32,51,16) or [[M(32,51,29]].</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>If <math>b</math> is in M(32,51,16), then <math>B</math> is in M(32,51,16) or [[M(32,51,29<ins class="diffchange diffchange-inline">)</ins>]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Projective indecomposable modules ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Projective indecomposable modules ==</div></td></tr>
</table>
CesareGArdito
http://wiki.manchester.ac.uk/blocks/index.php?title=M(32,51,16)&diff=1025&oldid=prev
CesareGArdito: /* Projective indecomposable modules */
2019-12-08T16:16:05Z
<p><span dir="auto"><span class="autocomment">Projective indecomposable modules</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr style="vertical-align: top;" lang="en-GB">
<td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 16:16, 8 December 2019</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43" >Line 43:</td>
<td colspan="2" class="diff-lineno">Line 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Labelling the simple <math>B</math>-modules by <math>S_1, \dots, S_{21}</math>, the projective indecomposable modules have Loewy structure as follows:</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Labelling the simple <math>B</math>-modules by <math>S_1, \dots, S_{21}</math>, the projective indecomposable modules have Loewy structure as follows:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math><del class="diffchange diffchange-inline">\begin{array}{cc}</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{1} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{1} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l56" >Line 56:</td>
<td colspan="2" class="diff-lineno">Line 56:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{4} S_{5} S_{2} S_{6} S_{3} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{4} S_{5} S_{2} S_{6} S_{3} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{1} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{1} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}<ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{2} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{2} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l71" >Line 71:</td>
<td colspan="2" class="diff-lineno">Line 70:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{2} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{2} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\end{array}</del></math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div></math> <math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"><br>&nbsp;<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math><del class="diffchange diffchange-inline">\begin{array}{cc}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{3} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{3} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l89" >Line 89:</td>
<td colspan="2" class="diff-lineno">Line 84:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{3} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{3} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{4} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{4} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l103" >Line 103:</td>
<td colspan="2" class="diff-lineno">Line 98:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{4} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{4} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\end{array}</del></math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div></math> <math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"><br>&nbsp;<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\begin{array}{cccc}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{5} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{5} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l122" >Line 122:</td>
<td colspan="2" class="diff-lineno">Line 112:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{5} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{5} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{6} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{6} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l136" >Line 136:</td>
<td colspan="2" class="diff-lineno">Line 126:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{6} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{6} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{7} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{7} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l150" >Line 150:</td>
<td colspan="2" class="diff-lineno">Line 140:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{7} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{7} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{8} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{8} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l164" >Line 164:</td>
<td colspan="2" class="diff-lineno">Line 154:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{8} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{8} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>   <del class="diffchange diffchange-inline">\end{array}</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>   </math> <math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"><br>&nbsp;<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\begin{array}{cccc}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{9} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{9} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l184" >Line 184:</td>
<td colspan="2" class="diff-lineno">Line 168:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{9} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{9} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{10} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{10} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l198" >Line 198:</td>
<td colspan="2" class="diff-lineno">Line 182:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{10} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{10} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{11} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{11} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l212" >Line 212:</td>
<td colspan="2" class="diff-lineno">Line 196:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{11} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{11} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{12} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{12} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l226" >Line 226:</td>
<td colspan="2" class="diff-lineno">Line 210:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{12} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{12} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>   <del class="diffchange diffchange-inline">\end{array}</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>   </math> <math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"><br>&nbsp;<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\begin{array}{cccc}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{13} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{13} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l246" >Line 246:</td>
<td colspan="2" class="diff-lineno">Line 224:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{13} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{13} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{14} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{14} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l260" >Line 260:</td>
<td colspan="2" class="diff-lineno">Line 238:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{14} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{14} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{15} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{15} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l274" >Line 274:</td>
<td colspan="2" class="diff-lineno">Line 252:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{15} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{15} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{16} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{16} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l288" >Line 288:</td>
<td colspan="2" class="diff-lineno">Line 266:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{16} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{16} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">  \end{array}</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </ins></math> <math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"><br>&nbsp;<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\begin{array}{ccccc}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{17} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{17} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l308" >Line 308:</td>
<td colspan="2" class="diff-lineno">Line 280:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{17} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{17} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{18} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{18} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l322" >Line 322:</td>
<td colspan="2" class="diff-lineno">Line 294:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{18} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{18} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{19} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{19} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l336" >Line 336:</td>
<td colspan="2" class="diff-lineno">Line 308:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{19} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{19} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{20} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{20} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l350" >Line 350:</td>
<td colspan="2" class="diff-lineno">Line 322:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{20} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{20} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></math> <math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{c}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{21} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{21} \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l364" >Line 364:</td>
<td colspan="2" class="diff-lineno">Line 336:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{21} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>S_{21} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   \end{array}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">  \end{array}</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">  </ins></math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Irreducible characters ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Irreducible characters ==</div></td></tr>
</table>
CesareGArdito
http://wiki.manchester.ac.uk/blocks/index.php?title=M(32,51,16)&diff=1024&oldid=prev
CesareGArdito: Created page with "{{blockbox |title = M(32,51,16) - <math>B_0(k(SL_2(8) \times A_5))</math> |image = |representative = <math>B_0(k(SL_2(8) \times A_5))</math> |defect = (C2)%5E5|<ma..."
2019-12-08T15:50:38Z
<p>Created page with "{{blockbox |title = M(32,51,16) - <math>B_0(k(SL_2(8) \times A_5))</math> |image = |representative = <math>B_0(k(SL_2(8) \times A_5))</math> |defect = (C2)%5E5|<ma..."</p>
<p><b>New page</b></p><div>{{blockbox<br />
|title = M(32,51,16) - <math>B_0(k(SL_2(8) \times A_5))</math> <br />
|image = &nbsp; <br />
|representative = <math>B_0(k(SL_2(8) \times A_5))</math><br />
|defect = [[(C2)%5E5|<math>(C_2)^5</math>]]<br />
|inertialquotients = <math>C_{21}</math><br />
|k(B) = 32<br />
|l(B) = 21<br />
|k-morita-frob = 1 <br />
|Pic-k= &nbsp;<br />
|cartan = See below.<br />
|defect-morita-inv? = Yes<br />
|inertial-morita-inv? = Yes<br />
|O-morita? = Yes<br />
|O-morita = <math>B_0(\mathcal{O} (SL_2(8) \times A_5))</math><br />
|decomp = See below.<br />
|O-morita-frob = 1<br />
|Pic-O = <br />
|PIgroup = <br />
|source? = No<br />
|sourcereps =<br />
|k-derived-known? = Yes<br />
|k-derived = [[M(32,51,13)]], [[M(32,51,14)]], [[M(32,51,15)]]<br />
|O-derived-known? = Yes<br />
|coveringblocks =<br />
|coveredblocks =<br />
|pcoveringblocks =<br />
}}<br />
<br />
<br />
== Basic algebra ==<br />
<br />
== Other notatable representatives ==<br />
<br />
== Covering blocks and covered blocks ==<br />
<br />
Let <math>N \triangleleft G</math> with prime <math>p'</math>-index and let <math>B</math> be a block of <math>\mathcal{O} G</math> covering a block <math>b</math> of <math>\mathcal{O} N</math>.<br />
<br />
If <math>b</math> is in M(32,51,16), then <math>B</math> is in M(32,51,16) or [[M(32,51,29]].<br />
<br />
== Projective indecomposable modules ==<br />
<br />
Labelling the simple <math>B</math>-modules by <math>S_1, \dots, S_{21}</math>, the projective indecomposable modules have Loewy structure as follows:<br />
<br />
<math>\begin{array}{cc}<br />
\begin{array}{c}<br />
S_{1} \\<br />
S_{5} S_{3} S_{6} S_{4} S_{2} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{11} S_{14} S_{9} S_{13} S_{16} S_{15} S_{8} S_{10} S_{12} \\<br />
S_{2} S_{4} S_{5} S_{5} S_{3} S_{4} S_{2} S_{4} S_{4} S_{6} S_{3} S_{2} S_{3} S_{2} S_{5} S_{5} S_{6} S_{3} S_{6} S_{6} S_{19} S_{7} S_{20} S_{18} S_{21} S_{17} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{11} S_{15} S_{9} S_{11} S_{12} S_{16} S_{8} S_{15} S_{12} S_{13} S_{10} S_{14} S_{15} S_{14} S_{16} S_{9} S_{9} S_{13} S_{13} S_{10} S_{12} S_{8} S_{8} S_{11} S_{14} S_{10} S_{16} \\<br />
S_{6} S_{6} S_{4} S_{3} S_{3} S_{6} S_{5} S_{3} S_{6} S_{3} S_{3} S_{6} S_{6} S_{4} S_{2} S_{2} S_{4} S_{4} S_{4} S_{5} S_{5} S_{3} S_{5} S_{2} S_{2} S_{2} S_{2} S_{5} S_{5} S_{4} S_{7} S_{19} S_{7} S_{17} S_{18} S_{17} S_{20} S_{20} S_{21} S_{18} S_{19} S_{21} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{14} S_{15} S_{9} S_{10} S_{13} S_{13} S_{12} S_{8} S_{15} S_{13} S_{16} S_{10} S_{10} S_{16} S_{15} S_{8} S_{8} S_{12} S_{11} S_{9} S_{11} S_{14} S_{16} S_{9} S_{11} S_{12} S_{14} \\<br />
S_{4} S_{2} S_{6} S_{5} S_{6} S_{4} S_{6} S_{2} S_{3} S_{3} S_{2} S_{6} S_{2} S_{5} S_{3} S_{4} S_{3} S_{5} S_{4} S_{5} S_{7} S_{18} S_{20} S_{19} S_{21} S_{17} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{13} S_{9} S_{10} S_{8} S_{11} S_{12} S_{14} S_{15} S_{16} \\<br />
S_{4} S_{5} S_{2} S_{6} S_{3} \\<br />
S_{1} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{2} \\<br />
S_{1} S_{12} S_{16} S_{14} \\<br />
S_{2} S_{4} S_{3} S_{5} S_{2} S_{2} S_{6} S_{20} S_{18} S_{7} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{8} S_{12} S_{14} S_{16} S_{15} S_{10} S_{12} S_{14} S_{13} S_{9} S_{16} S_{11} \\<br />
S_{3} S_{4} S_{4} S_{4} S_{5} S_{5} S_{6} S_{6} S_{2} S_{2} S_{5} S_{2} S_{3} S_{6} S_{3} S_{2} S_{21} S_{18} S_{19} S_{7} S_{17} S_{20} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{13} S_{15} S_{9} S_{10} S_{8} S_{12} S_{15} S_{8} S_{9} S_{14} S_{12} S_{16} S_{16} S_{10} S_{13} S_{11} S_{11} S_{14} \\<br />
S_{5} S_{6} S_{5} S_{2} S_{6} S_{2} S_{5} S_{4} S_{2} S_{4} S_{3} S_{3} S_{6} S_{3} S_{2} S_{4} S_{18} S_{21} S_{17} S_{20} S_{19} S_{7} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{10} S_{8} S_{14} S_{15} S_{14} S_{11} S_{13} S_{16} S_{9} S_{16} S_{12} S_{12} \\<br />
S_{2} S_{6} S_{3} S_{5} S_{2} S_{2} S_{4} S_{20} S_{7} S_{18} \\<br />
S_{1} S_{12} S_{14} S_{16} \\<br />
S_{2} \\<br />
\end{array}<br />
\end{array}</math><br />
<br />
<br>&nbsp;<br><br />
<br />
<math>\begin{array}{cc}<br />
\begin{array}{c}<br />
S_{3} \\<br />
S_{1} S_{11} S_{15} S_{13} \\<br />
S_{4} S_{3} S_{2} S_{5} S_{6} S_{3} S_{3} S_{19} S_{17} S_{21} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{16} S_{15} S_{14} S_{9} S_{11} S_{10} S_{12} S_{15} S_{11} S_{8} S_{13} S_{13} \\<br />
S_{3} S_{6} S_{2} S_{5} S_{3} S_{5} S_{5} S_{2} S_{6} S_{3} S_{2} S_{4} S_{4} S_{6} S_{3} S_{4} S_{19} S_{18} S_{17} S_{7} S_{20} S_{21} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{10} S_{9} S_{10} S_{13} S_{13} S_{16} S_{11} S_{8} S_{12} S_{8} S_{12} S_{16} S_{15} S_{15} S_{11} S_{9} S_{14} S_{14} \\<br />
S_{5} S_{6} S_{2} S_{5} S_{5} S_{3} S_{3} S_{3} S_{6} S_{2} S_{2} S_{4} S_{6} S_{4} S_{4} S_{3} S_{19} S_{21} S_{20} S_{17} S_{7} S_{18} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{9} S_{10} S_{11} S_{16} S_{14} S_{8} S_{15} S_{11} S_{13} S_{12} S_{15} S_{13} \\<br />
S_{4} S_{2} S_{3} S_{5} S_{6} S_{3} S_{3} S_{17} S_{19} S_{21} \\<br />
S_{1} S_{11} S_{15} S_{13} \\<br />
S_{3} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{4} \\<br />
S_{1} S_{14} S_{8} S_{13} \\<br />
S_{2} S_{4} S_{5} S_{6} S_{4} S_{3} S_{4} S_{7} S_{19} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{14} S_{12} S_{15} S_{11} S_{8} S_{16} S_{8} S_{13} S_{10} S_{14} S_{13} \\<br />
S_{2} S_{2} S_{6} S_{6} S_{2} S_{4} S_{3} S_{6} S_{5} S_{3} S_{4} S_{5} S_{4} S_{3} S_{4} S_{5} S_{19} S_{7} S_{21} S_{18} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{14} S_{10} S_{13} S_{10} S_{15} S_{12} S_{13} S_{15} S_{11} S_{8} S_{8} S_{16} S_{16} S_{11} S_{12} S_{14} \\<br />
S_{4} S_{4} S_{4} S_{2} S_{2} S_{3} S_{5} S_{3} S_{6} S_{4} S_{2} S_{5} S_{6} S_{5} S_{3} S_{6} S_{7} S_{21} S_{19} S_{18} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{12} S_{14} S_{15} S_{14} S_{16} S_{10} S_{8} S_{13} S_{13} S_{8} S_{11} \\<br />
S_{4} S_{5} S_{4} S_{2} S_{3} S_{6} S_{4} S_{19} S_{7} \\<br />
S_{1} S_{13} S_{14} S_{8} \\<br />
S_{4} \\<br />
\end{array}<br />
\end{array}</math><br />
<br />
<br>&nbsp;<br><br />
<br />
<math><br />
\begin{array}{cccc}<br />
\begin{array}{c}<br />
S_{5} \\<br />
S_{1} S_{15} S_{9} S_{12} \\<br />
S_{2} S_{6} S_{5} S_{5} S_{4} S_{5} S_{3} S_{20} S_{17} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{15} S_{13} S_{15} S_{9} S_{14} S_{9} S_{12} S_{8} S_{16} S_{12} S_{11} \\<br />
S_{2} S_{2} S_{6} S_{6} S_{6} S_{3} S_{3} S_{5} S_{4} S_{5} S_{2} S_{4} S_{3} S_{5} S_{4} S_{5} S_{7} S_{17} S_{19} S_{20} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{12} S_{12} S_{14} S_{11} S_{13} S_{16} S_{14} S_{15} S_{8} S_{11} S_{15} S_{16} S_{9} S_{9} S_{13} S_{8} \\<br />
S_{4} S_{2} S_{4} S_{5} S_{5} S_{4} S_{2} S_{2} S_{6} S_{5} S_{3} S_{3} S_{6} S_{5} S_{6} S_{3} S_{17} S_{20} S_{19} S_{7} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{13} S_{16} S_{15} S_{9} S_{14} S_{11} S_{12} S_{12} S_{9} S_{8} S_{15} \\<br />
S_{5} S_{5} S_{2} S_{4} S_{5} S_{3} S_{6} S_{17} S_{20} \\<br />
S_{1} S_{15} S_{12} S_{9} \\<br />
S_{5} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{6} \\<br />
S_{1} S_{11} S_{10} S_{16} \\<br />
S_{6} S_{6} S_{5} S_{4} S_{6} S_{2} S_{3} S_{18} S_{21} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{9} S_{13} S_{11} S_{16} S_{11} S_{16} S_{12} S_{10} S_{15} S_{14} S_{10} \\<br />
S_{4} S_{4} S_{6} S_{5} S_{2} S_{6} S_{4} S_{5} S_{3} S_{6} S_{6} S_{2} S_{2} S_{3} S_{5} S_{3} S_{18} S_{20} S_{21} S_{17} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{1} S_{1} S_{16} S_{14} S_{13} S_{16} S_{10} S_{9} S_{10} S_{14} S_{12} S_{15} S_{13} S_{15} S_{9} S_{12} S_{11} S_{11} \\<br />
S_{4} S_{2} S_{6} S_{6} S_{3} S_{2} S_{4} S_{3} S_{4} S_{5} S_{6} S_{5} S_{5} S_{6} S_{2} S_{3} S_{21} S_{20} S_{17} S_{18} \\<br />
S_{1} S_{1} S_{1} S_{1} S_{12} S_{16} S_{16} S_{14} S_{15} S_{11} S_{13} S_{11} S_{9} S_{10} S_{10} \\<br />
S_{5} S_{6} S_{6} S_{2} S_{3} S_{6} S_{4} S_{21} S_{18} \\<br />
S_{1} S_{11} S_{16} S_{10} \\<br />
S_{6} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{7} \\<br />
S_{8} S_{14} \\<br />
S_{2} S_{4} S_{19} \\<br />
S_{1} S_{13} S_{8} S_{12} \\<br />
S_{2} S_{3} S_{4} S_{5} S_{7} \\<br />
S_{1} S_{1} S_{15} S_{14} S_{14} \\<br />
S_{5} S_{3} S_{4} S_{2} S_{7} \\<br />
S_{1} S_{12} S_{8} S_{13} \\<br />
S_{4} S_{2} S_{19} \\<br />
S_{14} S_{8} \\<br />
S_{7} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{8} \\<br />
S_{4} S_{19} S_{7} \\<br />
S_{1} S_{8} S_{13} S_{8} S_{14} \\<br />
S_{3} S_{4} S_{4} S_{2} S_{5} S_{7} S_{19} \\<br />
S_{1} S_{1} S_{1} S_{14} S_{15} S_{8} S_{13} S_{12} \\<br />
S_{5} S_{5} S_{4} S_{2} S_{4} S_{3} S_{2} S_{3} \\<br />
S_{1} S_{1} S_{1} S_{14} S_{12} S_{13} S_{15} S_{8} \\<br />
S_{4} S_{3} S_{2} S_{5} S_{4} S_{19} S_{7} \\<br />
S_{1} S_{14} S_{13} S_{8} S_{8} \\<br />
S_{4} S_{7} S_{19} \\<br />
S_{8} \\<br />
\end{array}<br />
\end{array}<br />
</math><br />
<br />
<br>&nbsp;<br><br />
<br />
<math><br />
\begin{array}{cccc}<br />
\begin{array}{c}<br />
S_{9} \\<br />
S_{5} S_{17} S_{20} \\<br />
S_{1} S_{12} S_{15} S_{9} S_{9} \\<br />
S_{5} S_{5} S_{3} S_{2} S_{6} S_{20} S_{17} \\<br />
S_{1} S_{1} S_{1} S_{12} S_{11} S_{9} S_{15} S_{16} \\<br />
S_{3} S_{5} S_{2} S_{5} S_{3} S_{6} S_{6} S_{2} \\<br />
S_{1} S_{1} S_{1} S_{15} S_{12} S_{16} S_{9} S_{11} \\<br />
S_{5} S_{2} S_{6} S_{3} S_{5} S_{17} S_{20} \\<br />
S_{1} S_{9} S_{9} S_{15} S_{12} \\<br />
S_{5} S_{17} S_{20} \\<br />
S_{9} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{10} \\<br />
S_{6} S_{18} S_{21} \\<br />
S_{1} S_{10} S_{10} S_{16} S_{11} \\<br />
S_{3} S_{2} S_{4} S_{6} S_{6} S_{18} S_{21} \\<br />
S_{1} S_{1} S_{1} S_{10} S_{13} S_{11} S_{16} S_{14} \\<br />
S_{2} S_{3} S_{3} S_{2} S_{4} S_{4} S_{6} S_{6} \\<br />
S_{1} S_{1} S_{1} S_{11} S_{13} S_{14} S_{10} S_{16} \\<br />
S_{3} S_{4} S_{6} S_{2} S_{6} S_{18} S_{21} \\<br />
S_{1} S_{10} S_{16} S_{11} S_{10} \\<br />
S_{6} S_{18} S_{21} \\<br />
S_{10} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{11} \\<br />
S_{3} S_{6} S_{21} \\<br />
S_{1} S_{11} S_{15} S_{13} S_{10} S_{16} \\<br />
S_{5} S_{3} S_{2} S_{4} S_{6} S_{6} S_{3} S_{18} S_{17} \\<br />
S_{1} S_{1} S_{1} S_{9} S_{14} S_{11} S_{15} S_{12} S_{16} S_{13} S_{10} S_{11} \\<br />
S_{4} S_{3} S_{6} S_{5} S_{3} S_{5} S_{2} S_{6} S_{4} S_{2} S_{20} S_{21} S_{21} \\<br />
S_{1} S_{1} S_{1} S_{11} S_{16} S_{10} S_{14} S_{12} S_{9} S_{13} S_{11} S_{15} \\<br />
S_{6} S_{2} S_{6} S_{5} S_{4} S_{3} S_{3} S_{18} S_{17} \\<br />
S_{1} S_{16} S_{15} S_{10} S_{11} S_{13} \\<br />
S_{6} S_{3} S_{21} \\<br />
S_{11} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{12} \\<br />
S_{2} S_{5} S_{20} \\<br />
S_{1} S_{14} S_{16} S_{15} S_{12} S_{9} \\<br />
S_{5} S_{2} S_{6} S_{2} S_{4} S_{3} S_{5} S_{17} S_{7} \\<br />
S_{1} S_{1} S_{1} S_{15} S_{12} S_{16} S_{11} S_{8} S_{13} S_{14} S_{9} S_{12} \\<br />
S_{4} S_{4} S_{2} S_{6} S_{5} S_{3} S_{5} S_{2} S_{6} S_{3} S_{20} S_{19} S_{20} \\<br />
S_{1} S_{1} S_{1} S_{11} S_{9} S_{12} S_{13} S_{15} S_{8} S_{16} S_{14} S_{12} \\<br />
S_{5} S_{3} S_{5} S_{4} S_{6} S_{2} S_{2} S_{17} S_{7} \\<br />
S_{1} S_{14} S_{9} S_{12} S_{15} S_{16} \\<br />
S_{5} S_{2} S_{20} \\<br />
S_{12} \\<br />
\end{array}<br />
\end{array}<br />
</math><br />
<br />
<br>&nbsp;<br><br />
<br />
<math><br />
\begin{array}{cccc}<br />
\begin{array}{c}<br />
S_{13} \\<br />
S_{3} S_{4} S_{19} \\<br />
S_{1} S_{13} S_{11} S_{15} S_{8} S_{14} \\<br />
S_{6} S_{3} S_{2} S_{5} S_{4} S_{3} S_{4} S_{7} S_{21} \\<br />
S_{1} S_{1} S_{1} S_{10} S_{15} S_{13} S_{16} S_{12} S_{11} S_{14} S_{8} S_{13} \\<br />
S_{4} S_{5} S_{5} S_{6} S_{3} S_{2} S_{3} S_{6} S_{4} S_{2} S_{19} S_{18} S_{19} \\<br />
S_{1} S_{1} S_{1} S_{12} S_{8} S_{13} S_{15} S_{14} S_{10} S_{16} S_{11} S_{13} \\<br />
S_{2} S_{3} S_{3} S_{5} S_{4} S_{6} S_{4} S_{21} S_{7} \\<br />
S_{1} S_{15} S_{8} S_{13} S_{11} S_{14} \\<br />
S_{4} S_{3} S_{19} \\<br />
S_{13} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{14} \\<br />
S_{2} S_{4} S_{7} \\<br />
S_{1} S_{16} S_{12} S_{14} S_{8} S_{13} \\<br />
S_{3} S_{2} S_{4} S_{4} S_{5} S_{6} S_{2} S_{19} S_{18} \\<br />
S_{1} S_{1} S_{1} S_{16} S_{15} S_{10} S_{13} S_{11} S_{14} S_{12} S_{8} S_{14} \\<br />
S_{5} S_{2} S_{6} S_{4} S_{5} S_{3} S_{2} S_{4} S_{6} S_{3} S_{7} S_{21} S_{7} \\<br />
S_{1} S_{1} S_{1} S_{8} S_{11} S_{15} S_{16} S_{13} S_{10} S_{12} S_{14} S_{14} \\<br />
S_{6} S_{3} S_{4} S_{5} S_{4} S_{2} S_{2} S_{19} S_{18} \\<br />
S_{1} S_{12} S_{8} S_{13} S_{16} S_{14} \\<br />
S_{4} S_{2} S_{7} \\<br />
S_{14} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{15} \\<br />
S_{3} S_{5} S_{17} \\<br />
S_{1} S_{13} S_{9} S_{15} S_{11} S_{12} \\<br />
S_{3} S_{2} S_{4} S_{3} S_{5} S_{6} S_{5} S_{20} S_{19} \\<br />
S_{1} S_{1} S_{1} S_{15} S_{14} S_{13} S_{11} S_{16} S_{8} S_{12} S_{9} S_{15} \\<br />
S_{6} S_{3} S_{5} S_{5} S_{4} S_{2} S_{4} S_{2} S_{6} S_{3} S_{7} S_{17} S_{17} \\<br />
S_{1} S_{1} S_{1} S_{16} S_{15} S_{12} S_{14} S_{9} S_{8} S_{11} S_{15} S_{13} \\<br />
S_{5} S_{2} S_{3} S_{5} S_{4} S_{3} S_{6} S_{19} S_{20} \\<br />
S_{1} S_{12} S_{9} S_{11} S_{13} S_{15} \\<br />
S_{5} S_{3} S_{17} \\<br />
S_{15} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{16} \\<br />
S_{2} S_{6} S_{18} \\<br />
S_{1} S_{12} S_{14} S_{11} S_{10} S_{16} \\<br />
S_{3} S_{2} S_{4} S_{6} S_{5} S_{2} S_{6} S_{21} S_{20} \\<br />
S_{1} S_{1} S_{1} S_{14} S_{13} S_{9} S_{11} S_{16} S_{15} S_{12} S_{10} S_{16} \\<br />
S_{5} S_{2} S_{4} S_{6} S_{3} S_{3} S_{2} S_{6} S_{5} S_{4} S_{18} S_{17} S_{18} \\<br />
S_{1} S_{1} S_{1} S_{16} S_{10} S_{13} S_{15} S_{11} S_{9} S_{16} S_{14} S_{12} \\<br />
S_{3} S_{6} S_{6} S_{4} S_{5} S_{2} S_{2} S_{21} S_{20} \\<br />
S_{1} S_{10} S_{11} S_{14} S_{16} S_{12} \\<br />
S_{6} S_{2} S_{18} \\<br />
S_{16} \\<br />
\end{array}<br />
\end{array}<br />
</math><br />
<br />
<br>&nbsp;<br><br />
<br />
<math><br />
\begin{array}{ccccc}<br />
\begin{array}{c}<br />
S_{17} \\<br />
S_{15} S_{9} \\<br />
S_{3} S_{5} S_{20} \\<br />
S_{1} S_{12} S_{9} S_{11} \\<br />
S_{2} S_{3} S_{6} S_{5} S_{17} \\<br />
S_{1} S_{1} S_{16} S_{15} S_{15} \\<br />
S_{2} S_{5} S_{3} S_{6} S_{17} \\<br />
S_{1} S_{12} S_{11} S_{9} \\<br />
S_{5} S_{3} S_{20} \\<br />
S_{9} S_{15} \\<br />
S_{17} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{18} \\<br />
S_{16} S_{10} \\<br />
S_{6} S_{2} S_{21} \\<br />
S_{1} S_{10} S_{14} S_{11} \\<br />
S_{6} S_{3} S_{4} S_{2} S_{18} \\<br />
S_{1} S_{1} S_{16} S_{16} S_{13} \\<br />
S_{4} S_{3} S_{2} S_{6} S_{18} \\<br />
S_{1} S_{11} S_{10} S_{14} \\<br />
S_{2} S_{6} S_{21} \\<br />
S_{10} S_{16} \\<br />
S_{18} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{19} \\<br />
S_{8} S_{13} \\<br />
S_{3} S_{4} S_{7} \\<br />
S_{1} S_{14} S_{8} S_{15} \\<br />
S_{5} S_{3} S_{2} S_{4} S_{19} \\<br />
S_{1} S_{1} S_{13} S_{13} S_{12} \\<br />
S_{4} S_{2} S_{5} S_{3} S_{19} \\<br />
S_{1} S_{15} S_{14} S_{8} \\<br />
S_{4} S_{3} S_{7} \\<br />
S_{8} S_{13} \\<br />
S_{19} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{20} \\<br />
S_{12} S_{9} \\<br />
S_{2} S_{5} S_{17} \\<br />
S_{1} S_{16} S_{9} S_{15} \\<br />
S_{2} S_{3} S_{5} S_{6} S_{20} \\<br />
S_{1} S_{1} S_{12} S_{12} S_{11} \\<br />
S_{3} S_{5} S_{2} S_{6} S_{20} \\<br />
S_{1} S_{9} S_{15} S_{16} \\<br />
S_{5} S_{2} S_{17} \\<br />
S_{9} S_{12} \\<br />
S_{20} \\<br />
\end{array}<br />
&<br />
\begin{array}{c}<br />
S_{21} \\<br />
S_{11} S_{10} \\<br />
S_{3} S_{6} S_{18} \\<br />
S_{1} S_{13} S_{10} S_{16} \\<br />
S_{4} S_{6} S_{2} S_{3} S_{21} \\<br />
S_{1} S_{1} S_{14} S_{11} S_{11} \\<br />
S_{4} S_{6} S_{3} S_{2} S_{21} \\<br />
S_{1} S_{16} S_{13} S_{10} \\<br />
S_{6} S_{3} S_{18} \\<br />
S_{10} S_{11} \\<br />
S_{21} \\<br />
\end{array}<br />
\end{array}<br />
</math><br />
<br />
== Irreducible characters ==<br />
<br />
All irreducible characters have height zero.<br />
<br />
== Cartan matrix ==<br />
<math>\left( \begin{array}{ccccccccccccccccccccc}<br />
32 & 16 & 16 & 16 & 16 & 16 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 4 & 4 & 4 & 4 & 4 & 4 \\<br />
16 & 16 & 8 & 8 & 8 & 8 & 4 & 4 & 4 & 8 & 8 & 4 & 8 & 4 & 4 & 2 & 2 & 4 & 4 & 2 & 4 \\<br />
16 & 8 & 16 & 8 & 8 & 8 & 4 & 4 & 4 & 4 & 4 & 8 & 4 & 8 & 8 & 4 & 4 & 2 & 2 & 4 & 2 \\<br />
16 & 8 & 8 & 16 & 8 & 8 & 4 & 8 & 0 & 8 & 4 & 8 & 4 & 4 & 4 & 2 & 4 & 4 & 0 & 0 & 2 \\<br />
16 & 8 & 8 & 8 & 16 & 8 & 0 & 4 & 8 & 4 & 4 & 4 & 8 & 8 & 4 & 0 & 2 & 2 & 4 & 4 & 0 \\<br />
16 & 8 & 8 & 8 & 8 & 16 & 8 & 0 & 4 & 4 & 8 & 4 & 4 & 4 & 8 & 4 & 0 & 0 & 2 & 2 & 4 \\<br />
8 & 4 & 4 & 4 & 0 & 8 & 8 & 0 & 0 & 2 & 4 & 2 & 0 & 0 & 4 & 4 & 0 & 0 & 0 & 0 & 4 \\<br />
8 & 4 & 4 & 8 & 4 & 0 & 0 & 8 & 0 & 4 & 0 & 4 & 2 & 2 & 0 & 0 & 4 & 4 & 0 & 0 & 0 \\<br />
8 & 4 & 4 & 0 & 8 & 4 & 0 & 0 & 8 & 0 & 2 & 0 & 4 & 4 & 2 & 0 & 0 & 0 & 4 & 4 & 0 \\<br />
8 & 8 & 4 & 8 & 4 & 4 & 2 & 4 & 0 & 8 & 4 & 4 & 4 & 2 & 2 & 1 & 2 & 4 & 0 & 0 & 2 \\<br />
8 & 8 & 4 & 4 & 4 & 8 & 4 & 0 & 2 & 4 & 8 & 2 & 4 & 2 & 4 & 2 & 0 & 0 & 2 & 1 & 4 \\<br />
8 & 4 & 8 & 8 & 4 & 4 & 2 & 4 & 0 & 4 & 2 & 8 & 2 & 4 & 4 & 2 & 4 & 2 & 0 & 0 & 1 \\<br />
8 & 8 & 4 & 4 & 8 & 4 & 0 & 2 & 4 & 4 & 4 & 2 & 8 & 4 & 2 & 0 & 1 & 2 & 4 & 2 & 0 \\<br />
8 & 4 & 8 & 4 & 8 & 4 & 0 & 2 & 4 & 2 & 2 & 4 & 4 & 8 & 4 & 0 & 2 & 1 & 2 & 4 & 0 \\<br />
8 & 4 & 8 & 4 & 4 & 8 & 4 & 0 & 2 & 2 & 4 & 4 & 2 & 4 & 8 & 4 & 0 & 0 & 1 & 2 & 2 \\<br />
4 & 2 & 4 & 2 & 0 & 4 & 4 & 0 & 0 & 1 & 2 & 2 & 0 & 0 & 4 & 4 & 0 & 0 & 0 & 0 & 2 \\<br />
4 & 2 & 4 & 4 & 2 & 0 & 0 & 4 & 0 & 2 & 0 & 4 & 1 & 2 & 0 & 0 & 4 & 2 & 0 & 0 & 0 \\<br />
4 & 4 & 2 & 4 & 2 & 0 & 0 & 4 & 0 & 4 & 0 & 2 & 2 & 1 & 0 & 0 & 2 & 4 & 0 & 0 & 0 \\<br />
4 & 4 & 2 & 0 & 4 & 2 & 0 & 0 & 4 & 0 & 2 & 0 & 4 & 2 & 1 & 0 & 0 & 0 & 4 & 2 & 0 \\<br />
4 & 2 & 4 & 0 & 4 & 2 & 0 & 0 & 4 & 0 & 1 & 0 & 2 & 4 & 2 & 0 & 0 & 0 & 2 & 4 & 0 \\<br />
4 & 4 & 2 & 2 & 0 & 4 & 4 & 0 & 0 & 2 & 4 & 1 & 0 & 0 & 2 & 2 & 0 & 0 & 0 & 0 & 4 <br />
\end{array}\right)</math><br />
<br />
== Decomposition matrix ==<br />
<br />
<math>\left( \begin{array}{ccccccccccccccccccccc}<br />
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\<br />
1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\<br />
1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\<br />
1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\<br />
1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\<br />
1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\<br />
1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\<br />
1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\<br />
1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\<br />
1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\<br />
1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\<br />
1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 \\<br />
1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\<br />
1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\<br />
1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 \\<br />
1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1<br />
\end{array}\right)</math><br />
<br />
[[(C2)%5E5|Back to <math>(C_2)^5</math>]]</div>
CesareGArdito