L11a174: 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 = a | |
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k = 174 | |
k = 174 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,8,-6:4,-1,2,-3,7,-10,9,-8,5,-4,11,-9,10,-7,6,-5/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,8,-6:4,-1,2,-3,7,-10,9,-8,5,-4,11,-9,10,-7,6,-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:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.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:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr> |
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<tr><td>[[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:BraidPart2.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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khovanov_table = <table border=1> |
khovanov_table = <table border=1> |
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<tr align=center> |
<tr align=center> |
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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> |
</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, Alternating, 174]]]</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>2</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[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[16, 8, 17, 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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<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, Alternating, 174]]]</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>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[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[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[16, 8, 17, 7], |
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X[22, 16, 7, 15], X[6, 21, 1, 22], X[20, 11, 21, 12], |
X[22, 16, 7, 15], X[6, 21, 1, 22], X[20, 11, 21, 12], |
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X[14, 6, 15, 5], X[18, 13, 19, 14], X[12, 19, 13, 20], |
X[14, 6, 15, 5], X[18, 13, 19, 14], X[12, 19, 13, 20], |
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X[4, 18, 5, 17]]</nowiki></ |
X[4, 18, 5, 17]]</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[5]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[{1, -2, 3, -11, 8, -6}, |
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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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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</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>GaussCode[{1, -2, 3, -11, 8, -6}, |
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{4, -1, 2, -3, 7, -10, 9, -8, 5, -4, 11, -9, 10, -7, 6, -5}]</nowiki></ |
{4, -1, 2, -3, 7, -10, 9, -8, 5, -4, 11, -9, 10, -7, 6, -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[5, {1, -2, 3, -4, -3, -2, -1, -2, 3, -2, 4, 3, 3, -2, -2, -2, 3}]</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, Alternating, 174]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a174_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, Alternating, 174]]</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>-1</nowiki></pre></td></tr> |
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<tr align=left><td></td><td>[[Image:L11a174_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, Alternating, 174]][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> -(15/2) 3 6 11 14 17 17 15 |
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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, Alternating, 174]]</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>-1</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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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -(15/2) 3 6 11 14 17 17 15 |
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q - ----- + ----- - ---- + ---- - ---- + ---- - ------- + |
q - ----- + ----- - ---- + ---- - ---- + ---- - ------- + |
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13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q] |
13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q] |
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3/2 5/2 7/2 |
3/2 5/2 7/2 |
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11 Sqrt[q] - 7 q + 3 q - q</nowiki></ |
11 Sqrt[q] - 7 q + 3 q - q</nowiki></pre></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
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4 - q + q - q + q + --- - q + --- - q - q + q - |
4 - q + q - q + q + --- - q + --- - q - q + q - |
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14 10 |
14 10 |
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-- - q + q + 2 q - q + q |
-- - q + q + 2 q - q + q |
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2 |
2 |
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q</nowiki></ |
q</nowiki></pre></td></tr> |
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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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1 2 a 2 a a 3 z 5 3 z 3 |
1 2 a 2 a a 3 z 5 3 z 3 |
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-(---) + --- - ---- + -- - --- + 4 a z - 2 a z - ---- + 6 a z + |
-(---) + --- - ---- + -- - --- + 4 a z - 2 a z - ---- + 6 a z + |
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3 3 5 3 z 5 3 5 5 5 7 3 7 |
3 3 5 3 z 5 3 5 5 5 7 3 7 |
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5 a z - 3 a z - -- + 4 a z + 4 a z - a z + a z + a z |
5 a z - 3 a z - -- + 4 a z + 4 a z - a z + a z + a z |
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a</nowiki></ |
a</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 5 |
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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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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 5 |
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2 1 2 a 2 a a 5 z 3 7 2 |
2 1 2 a 2 a a 5 z 3 7 2 |
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-a - --- - --- - ---- - -- + --- + 8 a z + 2 a z + a z + 6 z + |
-a - --- - --- - ---- - -- + --- + 8 a z + 2 a z + a z + 6 z + |
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6 8 9 3 9 5 9 2 10 4 10 |
6 8 9 3 9 5 9 2 10 4 10 |
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4 a z - 5 a z - 9 a z - 4 a z - 2 a z - 2 a z</nowiki></ |
4 a z - 5 a z - 9 a z - 4 a z - 2 a z - 2 a z</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, Alternating, 174]][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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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
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9 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + |
9 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + |
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2 16 7 14 6 12 6 12 5 10 5 10 4 8 4 |
2 16 7 14 6 12 6 12 5 10 5 10 4 8 4 |
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2 2 4 2 4 3 6 3 8 4 |
2 2 4 2 4 3 6 3 8 4 |
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2 q t + 5 q t + q t + 2 q t + q t</nowiki></ |
2 q t + 5 q t + q t + 2 q t + q t</nowiki></pre></td></tr> |
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</table> }} |
</table> }} |
Revision as of 17:39, 2 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a174's Link Presentations]
Planar diagram presentation | X8192 X2,9,3,10 X10,3,11,4 X16,8,17,7 X22,16,7,15 X6,21,1,22 X20,11,21,12 X14,6,15,5 X18,13,19,14 X12,19,13,20 X4,18,5,17 |
Gauss code | {1, -2, 3, -11, 8, -6}, {4, -1, 2, -3, 7, -10, 9, -8, 5, -4, 11, -9, 10, -7, 6, -5} |
A Braid Representative | ||||||
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -1 (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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