L11n362: Difference between revisions
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n = 11 | |
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k = 362 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-11,5,-3:8,-4,-7,6,10,-9:4,-1,2,-5,-6,7,11,-2,3,-8,9,-10/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-11,5,-3:8,-4,-7,6,10,-9:4,-1,2,-5,-6,7,11,-2,3,-8,9,-10/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, NonAlternating, 362]]</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 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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<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[12, 7, 13, 8], X[4, 13, 1, 14], X[18, 6, 19, 5], |
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X[8, 4, 9, 3], X[9, 21, 10, 20], X[19, 11, 20, 10], |
X[8, 4, 9, 3], X[9, 21, 10, 20], X[19, 11, 20, 10], |
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X[14, 18, 15, 17], X[22, 16, 17, 15], X[16, 22, 5, 21], |
X[14, 18, 15, 17], X[22, 16, 17, 15], X[16, 22, 5, 21], |
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X[2, 12, 3, 11]]</nowiki></ |
X[2, 12, 3, 11]]</nowiki></code></td></tr> |
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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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{4, -1, 2, -5, -6, 7, 11, -2, 3, -8, 9, -10}]</nowiki></ |
{4, -1, 2, -5, -6, 7, 11, -2, 3, -8, 9, -10}]</nowiki></code></td></tr> |
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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, NonAlternating, 362]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11n362_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, NonAlternating, 362]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:L11n362_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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<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: 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[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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-7 - q + - + 11 q - 13 q + 14 q - 12 q + 10 q - 5 q + 3 q |
-7 - q + - + 11 q - 13 q + 14 q - 12 q + 10 q - 5 q + 3 q |
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q</nowiki></ |
q</nowiki></code></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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-q + -- + 3 q - 3 q + 2 q - q + q + 4 q + q + 7 q + |
-q + -- + 3 q - 3 q + 2 q - q + q + 4 q + q + 7 q + |
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4 |
4 |
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18 20 22 24 26 |
18 20 22 24 26 |
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3 q + 3 q + 4 q + q + q</nowiki></ |
3 q + 3 q + 4 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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-8 4 3 -2 1 2 1 2 3 z 4 z |
-8 4 3 -2 1 2 1 2 3 z 4 z |
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1 + a - -- + -- - a + ----- - ----- + ----- - z - ---- + ---- - |
1 + a - -- + -- - a + ----- - ----- + ----- - z - ---- + ---- - |
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z - -- + ---- + ---- + -- + -- |
z - -- + ---- + ---- + -- + -- |
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6 4 2 4 2 |
6 4 2 4 2 |
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a a a a a</nowiki></ |
a a 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><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Link[11, NonAlternating, 362]][a, z]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
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1 + -- + -- + -- + -- - ----- - ----- - ----- + ---- + ---- - ---- - |
1 + -- + -- + -- + -- - ----- - ----- - ----- + ---- + ---- - ---- - |
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8 6 4 2 8 2 6 2 4 2 7 5 7 |
8 6 4 2 8 2 6 2 4 2 7 5 7 |
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---- + ---- + ---- + ---- + ---- + ----- + ---- + ---- + ---- |
---- + ---- + ---- + ---- + ---- + ----- + ---- + ---- + ---- |
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7 5 3 a 6 4 2 5 3 |
7 5 3 a 6 4 2 5 3 |
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a a a a a a a a</nowiki></ |
a a a a a a a a</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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7 q + 6 q + ----- + ----- + ---- + --- + --- + 8 q t + 5 q t + |
7 q + 6 q + ----- + ----- + ---- + --- + --- + 8 q t + 5 q t + |
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5 3 3 2 2 q t t |
5 3 3 2 2 q t t |
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13 5 13 6 15 6 |
13 5 13 6 15 6 |
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4 q t + 2 q t + 3 q t</nowiki></ |
4 q t + 2 q t + 3 q t</nowiki></code></td></tr> |
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</table> }} |
Revision as of 18:14, 1 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11n362's Link Presentations]
Planar diagram presentation | X6172 X12,7,13,8 X4,13,1,14 X18,6,19,5 X8493 X9,21,10,20 X19,11,20,10 X14,18,15,17 X22,16,17,15 X16,22,5,21 X2,12,3,11 |
Gauss code | {1, -11, 5, -3}, {8, -4, -7, 6, 10, -9}, {4, -1, 2, -5, -6, 7, 11, -2, 3, -8, 9, -10} |
A Braid Representative | {{{braid_table}}} |
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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