L11a216: Difference between revisions
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n = 11 | |
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t = <nowiki>a</nowiki> | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-5,4,-11:10,-1,8,-9,11,-2,6,-3,5,-4,3,-6,7,-8,9,-7/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-5,4,-11:10,-1,8,-9,11,-2,6,-3,5,-4,3,-6,7,-8,9,-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 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, 216]]</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, 216]]]</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>2</nowiki></code></td></tr> |
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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[12, 3, 13, 4], X[14, 17, 15, 18], X[16, 5, 17, 6], |
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X[4, 15, 5, 16], X[18, 13, 19, 14], X[22, 19, 7, 20], |
X[4, 15, 5, 16], X[18, 13, 19, 14], X[22, 19, 7, 20], |
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X[20, 9, 21, 10], X[10, 21, 11, 22], X[2, 7, 3, 8], X[6, 11, 1, 12]]</nowiki></ |
X[20, 9, 21, 10], X[10, 21, 11, 22], X[2, 7, 3, 8], X[6, 11, 1, 12]]</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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{10, -1, 8, -9, 11, -2, 6, -3, 5, -4, 3, -6, 7, -8, 9, -7}]</nowiki></ |
{10, -1, 8, -9, 11, -2, 6, -3, 5, -4, 3, -6, 7, -8, 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, 216]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a216_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, 216]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:L11a216_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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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</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[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>-5</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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q - ----- + ----- - ----- + ----- - ----- + ----- - ----- + |
q - ----- + ----- - ----- + ----- - ----- + ----- - ----- + |
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25/2 23/2 21/2 19/2 17/2 15/2 13/2 |
25/2 23/2 21/2 19/2 17/2 15/2 13/2 |
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----- - ---- + ---- - q |
----- - ---- + ---- - q |
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11/2 9/2 7/2 |
11/2 9/2 7/2 |
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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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-q + --- - --- + q - --- + --- - q + --- + --- - q + --- - |
-q + --- - --- + q - --- + --- - q + --- + --- - q + --- - |
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38 36 30 28 24 22 18 |
38 36 30 28 24 22 18 |
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q + --- - --- + q |
q + --- - --- + q |
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12 10 |
12 10 |
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q q</nowiki></ |
q q</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>Out[10]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 7 9 11 |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</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> 7 9 11 |
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-2 a 3 a a 5 7 9 11 13 |
-2 a 3 a a 5 7 9 11 13 |
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----- + ---- - --- - a z - 7 a z + 3 a z + 3 a z - a z - |
----- + ---- - --- - a z - 7 a z + 3 a z + 3 a z - a z - |
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5 3 7 3 9 3 11 3 5 5 7 5 9 5 |
5 3 7 3 9 3 11 3 5 5 7 5 9 5 |
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2 a z - 8 a z - 2 a z + 3 a z - a z - 3 a z - 2 a z</nowiki></ |
2 a z - 8 a z - 2 a z + 3 a z - a z - 3 a z - 2 a z</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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8 10 12 2 a 3 a a 5 7 9 |
8 10 12 2 a 3 a a 5 7 9 |
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3 a + 3 a + a - ---- - ---- - --- - a z + 8 a z + 10 a z + |
3 a + 3 a + a - ---- - ---- - --- - a z + 8 a z + 10 a z + |
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11 9 13 9 10 10 12 10 |
11 9 13 9 10 10 12 10 |
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8 a z - 4 a z - a z - a z</nowiki></ |
8 a z - 4 a z - a z - a z</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[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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q + q + ------- + ------- + ------- + ------ + ------ + ------ + |
q + q + ------- + ------- + ------- + ------ + ------ + ------ + |
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28 11 26 10 24 10 24 9 22 9 22 8 |
28 11 26 10 24 10 24 9 22 9 22 8 |
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------ + ------ + ------ + ------ + ------ + ----- + ---- |
------ + ------ + ------ + ------ + ------ + ----- + ---- |
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14 4 12 4 12 3 10 3 10 2 8 2 6 |
14 4 12 4 12 3 10 3 10 2 8 2 6 |
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q t q t q t q t q t q t q t</nowiki></ |
q t q t q t q t q t q t q t</nowiki></code></td></tr> |
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</table> }} |
Revision as of 17:45, 1 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a216's Link Presentations]
Planar diagram presentation | X8192 X12,3,13,4 X14,17,15,18 X16,5,17,6 X4,15,5,16 X18,13,19,14 X22,19,7,20 X20,9,21,10 X10,21,11,22 X2738 X6,11,1,12 |
Gauss code | {1, -10, 2, -5, 4, -11}, {10, -1, 8, -9, 11, -2, 6, -3, 5, -4, 3, -6, 7, -8, 9, -7} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -5 (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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