L11n349: Difference between revisions
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{{Link Page| |
{{Link Page| |
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n = 11 | |
n = 11 | |
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t = |
t = n | |
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k = 349 | |
k = 349 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,4,-9,-6,7,3,-8:11,-2,-7,6,5,-4,8,-3,9,-5/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,4,-9,-6,7,3,-8:11,-2,-7,6,5,-4,8,-3,9,-5/goTop.html | |
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braid_table = <table cellspacing=0 cellpadding=0 border=0> |
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<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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khovanov_table = <table border=1> |
khovanov_table = <table border=1> |
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<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td> |
<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td> |
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</tr> |
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<tr valign=top><td colspan=2 |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 2, 2005, 15:8:39)...</td></tr> |
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</table> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>11</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<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>Length[Skeleton[Link[11, NonAlternating, 349]]]</nowiki></pre></td></tr> |
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<td>< |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>3</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[20, 12, 21, 11], X[18, 8, 19, 7], |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>11</nowiki></code></td></tr> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Length[Skeleton[Link[11, NonAlternating, 349]]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>3</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[20, 12, 21, 11], X[18, 8, 19, 7], |
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X[22, 18, 13, 17], X[9, 17, 10, 16], X[15, 11, 16, 10], |
X[22, 18, 13, 17], X[9, 17, 10, 16], X[15, 11, 16, 10], |
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X[12, 20, 5, 19], X[8, 22, 9, 21], X[2, 5, 3, 6], X[4, 13, 1, 14]]</nowiki></ |
X[12, 20, 5, 19], X[8, 22, 9, 21], X[2, 5, 3, 6], X[4, 13, 1, 14]]</nowiki></pre></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
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{11, -2, -7, 6, 5, -4, 8, -3, 9, -5}]</nowiki></ |
{11, -2, -7, 6, 5, -4, 8, -3, 9, -5}]</nowiki></pre></td></tr> |
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</table> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[6, {1, 2, -3, -4, -3, -5, -4, 3, 2, -1, 2, 3, 2, 4, -3, 5, 4, -3, 2}]</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<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>Show[DrawMorseLink[Link[11, NonAlternating, 349]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11n349_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[7]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td> |
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<td>< |
<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>KnotSignature[Link[11, NonAlternating, 349]]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>2</nowiki></pre></td></tr> |
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<tr align=left><td></td><td>[[Image:L11n349_ML.gif]]</td></tr><tr align=left> |
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< |
<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>J=Jones[Link[11, NonAlternating, 349]][q]</nowiki></pre></td></tr> |
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<td>< |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -3 2 6 2 3 4 5 6 |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>KnotSignature[Link[11, NonAlternating, 349]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>2</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td> |
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-8 + q - -- + - + 10 q - 10 q + 10 q - 7 q + 5 q - q |
-8 + q - -- + - + 10 q - 10 q + 10 q - 7 q + 5 q - q |
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2 q |
2 q |
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q</nowiki></ |
q</nowiki></pre></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
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2 + q + q + -- + 3 q + 5 q + q + 5 q + 3 q + q + 3 q - |
2 + q + q + -- + 3 q + 5 q + q + 5 q + 3 q + q + 3 q - |
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4 |
4 |
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18 |
18 |
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q</nowiki></ |
q</nowiki></pre></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td> |
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3 5 2 -2 1 2 2 2 z 2 2 4 |
3 5 2 -2 1 2 2 2 z 2 2 4 |
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-- - -- + 2 a + z + ----- - ----- - 4 z - ---- + a z - 2 z - |
-- - -- + 2 a + z + ----- - ----- - 4 z - ---- + a z - 2 z - |
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-- + ---- + -- |
-- + ---- + -- |
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4 2 2 |
4 2 2 |
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a a a</nowiki></ |
a a a</nowiki></pre></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
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3 - -- + -- + -- - 2 a - z - ----- - ----- + ---- + --- + -- - --- - |
3 - -- + -- + -- - 2 a - z - ----- - ----- + ---- + --- + -- - --- - |
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6 4 2 4 2 2 2 3 a z 5 3 |
6 4 2 4 2 2 2 3 a z 5 3 |
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2 a z + 3 z + ---- + ---- + -- + -- |
2 a z + 3 z + ---- + ---- + -- + -- |
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4 2 3 a |
4 2 3 a |
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a a a</nowiki></ |
a a a</nowiki></pre></td></tr> |
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<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>Kh[Link[11, NonAlternating, 349]][q, t]</nowiki></pre></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 1 1 2 4 2 4 4 q |
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6 q + 5 q + ----- + ----- + ----- + ----- + ---- + --- + --- + |
6 q + 5 q + ----- + ----- + ----- + ----- + ---- + --- + --- + |
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7 4 5 4 5 3 3 2 2 q t t |
7 4 5 4 5 3 3 2 2 q t t |
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11 4 13 5 |
11 4 13 5 |
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4 q t + q t</nowiki></ |
4 q t + q t</nowiki></pre></td></tr> |
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</table> }} |
</table> }} |
Revision as of 18:38, 2 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11n349's Link Presentations]
Planar diagram presentation | X6172 X14,3,15,4 X20,12,21,11 X18,8,19,7 X22,18,13,17 X9,17,10,16 X15,11,16,10 X12,20,5,19 X8,22,9,21 X2536 X4,13,1,14 |
Gauss code | {1, -10, 2, -11}, {10, -1, 4, -9, -6, 7, 3, -8}, {11, -2, -7, 6, 5, -4, 8, -3, 9, -5} |
A Braid Representative | |||||||
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | 2 (db) |
HOMFLY-PT polynomial | (db) |
Kauffman polynomial | (db) |
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). |
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Integral Khovanov Homology
(db, data source) |
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Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`
. See A Sample KnotTheory` Session.
Modifying This Page
Read me first: Modifying Knot Pages
See/edit the Link Page master template (intermediate). See/edit the Link_Splice_Base (expert). Back to the top. |
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