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K11a52 - Revision history
2026-05-13T12:32:52Z
Revision history for this page on the wiki
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https://katlas.org/index.php?title=K11a52&diff=110268&oldid=prev
DrorsRobot at 06:58, 3 September 2005
2005-09-03T06:58:12Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:58, 3 September 2005</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>k = 52 |</div></td>
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<td style="color: #202122; 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>braid_table = <table cellspacing=0 cellpadding=0 border=0<ins style="font-weight: bold; text-decoration: none;"> style="white-space: pre"</ins>></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </tr></div></td>
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<td style="color: #202122; 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> <tr valign=top><td colspan=2>Loading KnotTheory` (version of September <del style="font-weight: bold; text-decoration: none;">2</del>, 2005, <del style="font-weight: bold; text-decoration: none;">15</del>:<del style="font-weight: bold; text-decoration: none;">8</del>:<del style="font-weight: bold; text-decoration: none;">39</del>)...</td></tr> </div></td>
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<td style="color: #202122; 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> <tr valign=top><td colspan=2>Loading KnotTheory` (version of September <ins style="font-weight: bold; text-decoration: none;">3</ins>, 2005, <ins style="font-weight: bold; text-decoration: none;">2</ins>:<ins style="font-weight: bold; text-decoration: none;">11</ins>:<ins style="font-weight: bold; text-decoration: none;">43</ins>)...</td></tr> </div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Knot[11, Alternating, 52]]</nowiki></pre></td></tr></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Knot[11, Alternating, 52]]</nowiki></pre></td></tr></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>11</nowiki></pre></td></tr></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>11</nowiki></pre></td></tr></div></td>
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DrorsRobot
https://katlas.org/index.php?title=K11a52&diff=46510&oldid=prev
DrorsRobot at 21:19, 2 September 2005
2005-09-02T21:19:06Z
<p></p>
<a href="https://katlas.org/index.php?title=K11a52&diff=46510&oldid=44526">Show changes</a>
DrorsRobot
https://katlas.org/index.php?title=K11a52&diff=44526&oldid=prev
ScottTestRobot at 21:24, 1 September 2005
2005-09-01T21:24:56Z
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<a href="https://katlas.org/index.php?title=K11a52&diff=44526&oldid=42613">Show changes</a>
ScottTestRobot
https://katlas.org/index.php?title=K11a52&diff=42613&oldid=prev
ScottKnotPageRobot at 17:03, 30 August 2005
2005-08-30T17:03:17Z
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<a href="https://katlas.org/index.php?title=K11a52&diff=42613&oldid=37194">Show changes</a>
ScottKnotPageRobot
https://katlas.org/index.php?title=K11a52&diff=37194&oldid=prev
ScottTestRobot at 00:56, 29 August 2005
2005-08-29T00:56:39Z
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<p><b>New page</b></p><div><!-- --><br />
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{{Hoste-Thistlethwaite Knot Page Header|n=11|t=a|k=52|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-5,2,-1,3,-11,4,-2,5,-9,6,-4,7,-3,8,-10,9,-6,10,-8,11,-7/goTop.html}}<br />
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{{:{{PAGENAME}} Further Notes and Views}}<br />
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{{Knot Presentations}}<br />
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<tr><td>\</td><td>&nbsp;</td><td>r</td></tr><br />
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr><br />
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr><br />
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<td width=6.25%>-5</td ><td width=6.25%>-4</td ><td width=6.25%>-3</td ><td width=6.25%>-2</td ><td width=6.25%>-1</td ><td width=6.25%>0</td ><td width=6.25%>1</td ><td width=6.25%>2</td ><td width=6.25%>3</td ><td width=6.25%>4</td ><td width=6.25%>5</td ><td width=6.25%>6</td ><td width=12.5%>&chi;</td></tr><br />
<tr align=center><td>13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>1</td></tr><br />
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>&nbsp;</td><td>-4</td></tr><br />
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>5</td></tr><br />
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>9</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>-5</td></tr><br />
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>11</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>5</td></tr><br />
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>11</td><td bgcolor=yellow>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr><br />
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>11</td><td bgcolor=yellow>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr><br />
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>8</td><td bgcolor=yellow>12</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr><br />
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>10</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-5</td></tr><br />
<tr align=center><td>-5</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>8</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>6</td></tr><br />
<tr align=center><td>-7</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-4</td></tr><br />
<tr align=center><td>-9</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-11</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
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<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td><br />
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td><br />
</tr><br />
<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 17, 2005, 14:44:34)...</pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Knot[11, Alternating, 52]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>11</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[11, Alternating, 52]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[4, 2, 5, 1], X[8, 3, 9, 4], X[14, 5, 15, 6], X[12, 8, 13, 7], <br />
<br />
X[2, 9, 3, 10], X[18, 12, 19, 11], X[22, 13, 1, 14], <br />
<br />
X[20, 16, 21, 15], X[10, 18, 11, 17], X[16, 20, 17, 19], <br />
<br />
X[6, 21, 7, 22]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[11, Alternating, 52]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[1, -5, 2, -1, 3, -11, 4, -2, 5, -9, 6, -4, 7, -3, 8, -10, 9, <br />
<br />
-6, 10, -8, 11, -7]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BR[Knot[11, Alternating, 52]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[Knot[11, Alternating, 52]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[11, Alternating, 52]][t]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 13 32 2 3<br />
43 - -- + -- - -- - 32 t + 13 t - 2 t<br />
3 2 t<br />
t t</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[11, Alternating, 52]][z]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6<br />
1 + 2 z + z - 2 z</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[11, Alternating, 52]}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Knot[11, Alternating, 52]], KnotSignature[Knot[11, Alternating, 52]]}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{137, 0}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>J=Jones[Knot[11, Alternating, 52]][q]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -5 3 7 13 18 2 3 4 5 6<br />
22 - q + -- - -- + -- - -- - 22 q + 20 q - 15 q + 10 q - 5 q + q<br />
4 3 2 q<br />
q q q</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[11, Alternating, 52]}</nowiki></pre></td></tr><br />
<math>\textrm{Include}(\textrm{ColouredJonesM.mhtml})</math><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[11, Alternating, 52]][q]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -16 -12 3 3 2 3 4 2 4 6 8<br />
-3 - q + q - --- + -- + -- - -- + -- + 2 q + q - q + 5 q - <br />
10 8 6 4 2<br />
q q q q q<br />
<br />
10 12 14 16 18<br />
4 q + q + q - 3 q + q</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[11, Alternating, 52]][a, z]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2<br />
-4 2 2 4 z 3 z 5 2 2 z<br />
-1 - a - -- - 2 a - a + -- - --- - 3 a z + a z - z - ---- + <br />
2 5 a 2<br />
a a a<br />
<br />
3 3 3<br />
2 2 4 2 3 z 7 z 10 z 3 3 3<br />
4 a z + 3 a z + ---- + ---- + ----- + 10 a z + 2 a z - <br />
5 3 a<br />
a a<br />
<br />
4 4 4 5<br />
5 3 4 z 11 z 27 z 2 4 4 4 10 z<br />
2 a z + 19 z - -- + ----- + ----- - a z - 5 a z - ----- - <br />
6 4 2 5<br />
a a a a<br />
<br />
5 5 6 6 6<br />
9 z z 5 3 5 5 5 6 z 21 z 41 z<br />
---- - -- - 9 a z - 6 a z + a z - 27 z + -- - ----- - ----- - <br />
3 a 6 4 2<br />
a a a a<br />
<br />
7 7 7 8<br />
2 6 4 6 5 z 8 z 18 z 3 7 8 9 z<br />
5 a z + 3 a z + ---- - ---- - ----- + 5 a z + 11 z + ---- + <br />
5 3 a 4<br />
a a a<br />
<br />
8 9 9 10<br />
14 z 2 8 7 z 12 z 9 10 2 z<br />
----- + 6 a z + ---- + ----- + 5 a z + 2 z + -----<br />
2 3 a 2<br />
a a a</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[11, Alternating, 52]], Vassiliev[3][Knot[11, Alternating, 52]]}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 0}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[11, Alternating, 52]][q, t]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>12 1 2 1 5 2 8 5<br />
-- + 11 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + <br />
q 11 5 9 4 7 4 7 3 5 3 5 2 3 2<br />
q t q t q t q t q t q t q t<br />
<br />
10 8 3 3 2 5 2 5 3<br />
---- + --- + 11 q t + 11 q t + 9 q t + 11 q t + 6 q t + <br />
3 q t<br />
q t<br />
<br />
7 3 7 4 9 4 9 5 11 5 13 6<br />
9 q t + 4 q t + 6 q t + q t + 4 q t + q t</nowiki></pre></td></tr><br />
</table><br />
<br />
[[Category:Knot Page]]</div>
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