L11a456: Difference between revisions
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{{Link Page| |
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n = 11 | |
n = 11 | |
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t = a | |
t = <nowiki>a</nowiki> | |
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k = 456 | |
k = 456 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,4,-6,5,-8,3,-9:8,-2,11,-5,6,-4,7,-3,9,-7/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,4,-6,5,-8,3,-9:8,-2,11,-5,6,-4,7,-3,9,-7/goTop.html | |
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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>Loading KnotTheory` (version of August |
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr> |
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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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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</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>Crossings[Link[11, Alternating, 456]]</nowiki></code></td></tr> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</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>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, 456]]]</nowiki></code></td></tr> |
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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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<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, 4, 15, 3], X[20, 11, 21, 12], X[18, 8, 19, 7], |
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X[16, 10, 17, 9], X[8, 18, 9, 17], X[22, 19, 13, 20], |
X[16, 10, 17, 9], X[8, 18, 9, 17], X[22, 19, 13, 20], |
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X[10, 14, 11, 13], X[12, 21, 5, 22], X[2, 5, 3, 6], X[4, 16, 1, 15]]</nowiki></ |
X[10, 14, 11, 13], X[12, 21, 5, 22], X[2, 5, 3, 6], X[4, 16, 1, 15]]</nowiki></code></td></tr> |
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</table> |
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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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{8, -2, 11, -5, 6, -4, 7, -3, 9, -7}]</nowiki></ |
{8, -2, 11, -5, 6, -4, 7, -3, 9, -7}]</nowiki></code></td></tr> |
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</table> |
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<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>Show[DrawMorseLink[Link[11, Alternating, 456]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a456_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[6]=</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><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Link[11, Alternating, 456]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:L11a456_ML.gif]]</td></tr><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</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>-Graphics-</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[7]:=</code></td> |
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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>0</nowiki></code></td></tr> |
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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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19 - q + -- - -- + -- - -- - 18 q + 17 q - 11 q + 7 q - 3 q + q |
19 - q + -- - -- + -- - -- - 18 q + 17 q - 11 q + 7 q - 3 q + q |
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4 3 2 q |
4 3 2 q |
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q q q</nowiki></ |
q q q</nowiki></code></td></tr> |
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</table> |
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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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-1 - q + q - --- + -- + -- - q + -- + 5 q + 3 q + 3 q + |
-1 - q + q - --- + -- + -- - q + -- + 5 q + 3 q + 3 q + |
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10 8 6 2 |
10 8 6 2 |
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8 10 12 14 16 18 |
8 10 12 14 16 18 |
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7 q - q + 3 q + 2 q - q + q</nowiki></ |
7 q - q + 3 q + 2 q - q + q</nowiki></code></td></tr> |
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</table> |
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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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2 5 2 4 -2 1 2 2 2 z 6 z |
2 5 2 4 -2 1 2 2 2 z 6 z |
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2 + -- - -- + 2 a - a + z + ----- - ----- + z + ---- - ---- + |
2 + -- - -- + 2 a - a + z + ----- - ----- + z + ---- - ---- + |
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3 a z - a z - z + -- - ---- + 2 a z - z - -- |
3 a z - a z - z + -- - ---- + 2 a z - z - -- |
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4 2 2 |
4 2 2 |
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a a a</nowiki></ |
a a a</nowiki></code></td></tr> |
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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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9 + -- + -- - a - z - ----- - ----- + ---- + --- - --- - --- - |
9 + -- + -- - a - z - ----- - ----- + ---- + --- - --- - --- - |
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4 2 4 2 2 2 3 a z 3 a |
4 2 4 2 2 2 3 a z 3 a |
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6 a z + ---- + ---- + 4 a z + z + --- |
6 a z + ---- + ---- + 4 a z + z + --- |
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3 a 2 |
3 a 2 |
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a a</nowiki></ |
a a</nowiki></code></td></tr> |
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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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-- + 11 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + |
-- + 11 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + |
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q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 |
q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 |
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7 3 7 4 9 4 9 5 11 5 13 6 |
7 3 7 4 9 4 9 5 11 5 13 6 |
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7 q t + 3 q t + 5 q t + q t + 2 q t + q t</nowiki></ |
7 q t + 3 q t + 5 q t + q t + 2 q t + q t</nowiki></code></td></tr> |
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</table> }} |
Revision as of 18:37, 1 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a456's Link Presentations]
Planar diagram presentation | X6172 X14,4,15,3 X20,11,21,12 X18,8,19,7 X16,10,17,9 X8,18,9,17 X22,19,13,20 X10,14,11,13 X12,21,5,22 X2536 X4,16,1,15 |
Gauss code | {1, -10, 2, -11}, {10, -1, 4, -6, 5, -8, 3, -9}, {8, -2, 11, -5, 6, -4, 7, -3, 9, -7} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | 0 (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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