L11a87: Difference between revisions
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n = 11 | |
n = 11 | |
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t = <nowiki>a</nowiki> | |
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k = 87 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,5,-9,7,-3,11,-2,3,-6,8,-7,4,-5,6,-8,9,-4/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,5,-9,7,-3,11,-2,3,-6,8,-7,4,-5,6,-8,9,-4/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, 87]]</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, 87]]]</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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</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[12, 3, 13, 4], X[10, 14, 11, 13], X[22, 17, 5, 18], |
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X[18, 7, 19, 8], X[14, 20, 15, 19], X[16, 10, 17, 9], |
X[18, 7, 19, 8], X[14, 20, 15, 19], X[16, 10, 17, 9], |
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X[20, 16, 21, 15], X[8, 21, 9, 22], X[2, 5, 3, 6], X[4, 11, 1, 12]]</nowiki></ |
X[20, 16, 21, 15], X[8, 21, 9, 22], X[2, 5, 3, 6], X[4, 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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-7, 4, -5, 6, -8, 9, -4}]</nowiki></ |
-7, 4, -5, 6, -8, 9, -4}]</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, 87]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a87_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, 87]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:L11a87_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 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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<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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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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17 Sqrt[q] - 11 q + 5 q - q</nowiki></ |
17 Sqrt[q] - 11 q + 5 q - q</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[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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5 - q - q + q - --- + q + --- - q + --- + q - q + |
5 - q - q + q - --- + q + --- - q + --- + q - q + |
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18 14 10 |
18 14 10 |
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-- - -- - 3 q - q + 3 q - 3 q + q |
-- - -- - 3 q - q + 3 q - 3 q + q |
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4 2 |
4 2 |
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q q</nowiki></ |
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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a 4 a 4 a a 3 5 7 z 3 |
a 4 a 4 a a 3 5 7 z 3 |
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- - ---- + ---- - -- + 2 a z - 9 a z + 6 a z - a z - -- + 4 a z - |
- - ---- + ---- - -- + 2 a z - 9 a z + 6 a z - a z - -- + 4 a z - |
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3 3 5 3 z 5 3 5 7 |
3 3 5 3 z 5 3 5 7 |
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8 a z + 3 a z - -- + 3 a z - 3 a z + a z |
8 a z + 3 a z - -- + 3 a z - 3 a z + a z |
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a</nowiki></ |
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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2 4 6 8 a 4 a 4 a a 3 |
2 4 6 8 a 4 a 4 a a 3 |
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1 + 4 a + 7 a + 4 a + a - - - ---- - ---- - -- + 3 a z + 15 a z + |
1 + 4 a + 7 a + 4 a + a - - - ---- - ---- - -- + 3 a z + 15 a z + |
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2 10 4 10 |
2 10 4 10 |
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2 a z - 2 a z</nowiki></ |
2 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[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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12 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + |
12 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + |
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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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4 q t + 7 q t + q t + 4 q t + q t</nowiki></ |
4 q t + 7 q t + q t + 4 q t + q t</nowiki></code></td></tr> |
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</table> }} |
Revision as of 17:44, 1 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a87's Link Presentations]
Planar diagram presentation | X6172 X12,3,13,4 X10,14,11,13 X22,17,5,18 X18,7,19,8 X14,20,15,19 X16,10,17,9 X20,16,21,15 X8,21,9,22 X2536 X4,11,1,12 |
Gauss code | {1, -10, 2, -11}, {10, -1, 5, -9, 7, -3, 11, -2, 3, -6, 8, -7, 4, -5, 6, -8, 9, -4} |
A Braid Representative | {{{braid_table}}} |
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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