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L9a42 - Revision history
2026-05-20T11:59:07Z
Revision history for this page on the wiki
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https://katlas.org/index.php?title=L9a42&diff=110371&oldid=prev
DrorsRobot at 07:29, 3 September 2005
2005-09-03T07:29:18Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 03:29, 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 = 42 |</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:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]</td></tr></div></td>
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<td colspan="2" class="diff-lineno">Line 47:</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="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[Link[9, Alternating, 42]]</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[Link[9, Alternating, 42]]</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>9</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>9</nowiki></pre></td></tr></div></td>
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DrorsRobot
https://katlas.org/index.php?title=L9a42&diff=47198&oldid=prev
DrorsRobot at 22:57, 2 September 2005
2005-09-02T22:57:52Z
<p></p>
<a href="https://katlas.org/index.php?title=L9a42&diff=47198&oldid=45207">Show changes</a>
DrorsRobot
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ScottTestRobot at 22:46, 1 September 2005
2005-09-01T22:46:44Z
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<a href="https://katlas.org/index.php?title=L9a42&diff=45207&oldid=43532">Show changes</a>
ScottTestRobot
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DrorsRobot at 16:58, 31 August 2005
2005-08-31T16:58:38Z
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<a href="https://katlas.org/index.php?title=L9a42&diff=43532&oldid=40865">Show changes</a>
DrorsRobot
https://katlas.org/index.php?title=L9a42&diff=40865&oldid=prev
ScottKnotPageRobot at 17:25, 30 August 2005
2005-08-30T17:25:02Z
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<a href="https://katlas.org/index.php?title=L9a42&diff=40865&oldid=37249">Show changes</a>
ScottKnotPageRobot
https://katlas.org/index.php?title=L9a42&diff=37249&oldid=prev
ScottTestRobot at 01:12, 29 August 2005
2005-08-29T01:12:39Z
<p></p>
<p><b>New page</b></p><div><!-- --><br />
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{{Knot Navigation Links|ext=gif}}<br />
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{{Link Page Header|n=9|t=a|k=42|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-7,3,-4,6,-8:4,-1,5,-2,7,-6,8,-5,9,-3/goTop.html}}<br />
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{{:{{PAGENAME}} Further Notes and Views}}<br />
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{{Link Presentations}}<br />
{{Link Polynomial Invariants}}<br />
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{{Khovanov Homology|table=<table border=1><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=7.14286%>-4</td ><td width=7.14286%>-3</td ><td width=7.14286%>-2</td ><td width=7.14286%>-1</td ><td width=7.14286%>0</td ><td width=7.14286%>1</td ><td width=7.14286%>2</td ><td width=7.14286%>3</td ><td width=7.14286%>4</td ><td width=7.14286%>5</td ><td width=14.2857%>&chi;</td></tr><br />
<tr align=center><td>12</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>10</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>2</td><td bgcolor=yellow>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>8</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>1</td><td>&nbsp;</td><td>-3</td></tr><br />
<tr align=center><td>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr><br />
<tr align=center><td>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr><br />
<tr align=center><td>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>0</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>6</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>-2</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</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>-4</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr><br />
<tr align=center><td>-6</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>-2</td></tr><br />
<tr align=center><td>-8</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>1</td></tr><br />
</table>}}<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[Link[9, Alternating, 42]]</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>9</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[Link[9, Alternating, 42]]</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[10, 1, 11, 2], X[12, 4, 13, 3], X[18, 5, 9, 6], X[6, 9, 7, 10], <br />
<br />
X[16, 12, 17, 11], X[14, 8, 15, 7], X[4, 14, 5, 13], X[8, 16, 1, 15], <br />
<br />
X[2, 17, 3, 18]]</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[Link[9, Alternating, 42]]</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, -9, 2, -7, 3, -4, 6, -8}, <br />
<br />
{4, -1, 5, -2, 7, -6, 8, -5, 9, -3}]</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[Link[9, Alternating, 42]]</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[Link[9, Alternating, 42]]</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[Link[9, Alternating, 42]][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>ComplexInfinity</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[Link[9, Alternating, 42]][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>ComplexInfinity</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>{}</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[Link[9, Alternating, 42]], KnotSignature[Link[9, Alternating, 42]]}</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>{Infinity, 1}</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[Link[9, Alternating, 42]][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> -(7/2) 3 6 8 3/2 5/2<br />
-q + ---- - ---- + ------- - 10 Sqrt[q] + 9 q - 9 q + <br />
5/2 3/2 Sqrt[q]<br />
q q<br />
<br />
7/2 9/2 11/2<br />
6 q - 3 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>{}</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[Link[9, Alternating, 42]][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> -10 -8 2 2 4 8 10 12 14 16<br />
3 + q - q + -- - q + 4 q + 2 q + q - 2 q + q - q<br />
6<br />
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[Link[9, Alternating, 42]][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 2 2<br />
1 a z 2 z 6 z 3 2 z 3 z 6 z<br />
1 - --- - - - -- + --- + --- + 2 a z - a z - 5 z + -- - ---- - ---- - <br />
a z z 5 3 a 6 4 2<br />
a a a a a<br />
<br />
3 3 3 4<br />
2 2 3 z 4 z 12 z 3 3 3 4 z<br />
3 a z + ---- - ---- - ----- - 3 a z + 2 a z + 11 z - -- + <br />
5 3 a 6<br />
a a a<br />
<br />
4 4 5 5 5<br />
6 z 12 z 2 4 3 z 6 z 17 z 5 3 5<br />
---- + ----- + 6 a z - ---- + ---- + ----- + 7 a z - a z - <br />
4 2 5 3 a<br />
a a a a<br />
<br />
6 6 7 7 8<br />
6 5 z 5 z 2 6 5 z 9 z 7 8 2 z<br />
3 z - ---- - ---- - 3 a z - ---- - ---- - 4 a z - 2 z - ----<br />
4 2 3 a 2<br />
a 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][Link[9, Alternating, 42]], Vassiliev[3][Link[9, Alternating, 42]]}</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> 3<br />
{0, -(-)}<br />
2</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[Link[9, Alternating, 42]][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> 2 1 2 1 4 2 4 4 2<br />
6 + 6 q + ----- + ----- + ----- + ----- + ----- + - + ---- + 5 q t + <br />
8 4 6 3 4 3 4 2 2 2 t 2<br />
q t q t q t q t q t q t<br />
<br />
4 4 2 6 2 6 3 8 3 8 4 10 4<br />
4 q t + 4 q t + 5 q t + 2 q t + 4 q t + q t + 2 q t + <br />
<br />
12 5<br />
q t</nowiki></pre></td></tr><br />
</table><br />
<br />
[[Category:Knot Page]]</div>
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