L11n195: Difference between revisions
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-6,4,-5:5,-1,-8,9,2,-3,7,-11,6,-4,10,8,-9,-7,11,-10/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-6,4,-5:5,-1,-8,9,2,-3,7,-11,6,-4,10,8,-9,-7,11,-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, 195]]</nowiki></code></td></tr> |
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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: 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[2, 11, 3, 12], X[12, 3, 13, 4], X[16, 5, 17, 6], |
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X[6, 7, 1, 8], X[4, 15, 5, 16], X[20, 14, 21, 13], X[9, 18, 10, 19], |
X[6, 7, 1, 8], X[4, 15, 5, 16], X[20, 14, 21, 13], X[9, 18, 10, 19], |
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X[19, 10, 20, 11], X[22, 18, 7, 17], X[14, 22, 15, 21]]</nowiki></ |
X[19, 10, 20, 11], X[22, 18, 7, 17], X[14, 22, 15, 21]]</nowiki></code></td></tr> |
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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, -6, 4, -5}, |
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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, -6, 4, -5}, |
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{5, -1, -8, 9, 2, -3, 7, -11, 6, -4, 10, 8, -9, -7, 11, -10}]</nowiki></ |
{5, -1, -8, 9, 2, -3, 7, -11, 6, -4, 10, 8, -9, -7, 11, -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, 195]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11n195_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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< |
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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, 195]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:L11n195_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>-3</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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17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2 |
17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2 |
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1 |
1 |
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------- |
------- |
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Sqrt[q]</nowiki></ |
Sqrt[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 - q + --- + --- - q + --- - q + q + -- - q + -- - q |
q - q + --- + --- - q + --- - q + q + -- - q + -- - q |
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24 18 14 8 4 |
24 18 14 8 4 |
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q q q q q</nowiki></ |
q q q q q</nowiki></code></td></tr> |
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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> 5 7 |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 5 7 |
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a a 5 7 3 3 5 3 7 3 3 5 |
a a 5 7 3 3 5 3 7 3 3 5 |
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-(--) + -- - 6 a z + 3 a z + 2 a z - 9 a z + 3 a z + a z - |
-(--) + -- - 6 a z + 3 a z + 2 a z - 9 a z + 3 a z + a z - |
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5 5 7 5 5 7 |
5 5 7 5 5 7 |
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5 a z + a z - a z</nowiki></ |
5 a z + a z - a z</nowiki></code></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 5 7 |
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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, 195]][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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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 5 7 |
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6 a a 5 7 9 11 2 2 4 2 |
6 a a 5 7 9 11 2 2 4 2 |
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-a + -- + -- - 6 a z - 4 a z + a z - a z + a z + 2 a z + |
-a + -- + -- - 6 a z - 4 a z + a z - a z + a z + 2 a z + |
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5 7 7 7 9 7 4 8 6 8 8 8 5 9 7 9 |
5 7 7 7 9 7 4 8 6 8 8 8 5 9 7 9 |
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a z - 3 a z - 4 a z - a z - 4 a z - 3 a z - a z - a z</nowiki></ |
a z - 3 a z - 4 a z - a z - 4 a z - 3 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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-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + |
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + |
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4 2 20 8 18 7 16 7 16 6 14 6 14 5 |
4 2 20 8 18 7 16 7 16 6 14 6 14 5 |
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---- + t |
---- + t |
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4 |
4 |
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q t</nowiki></ |
q t</nowiki></code></td></tr> |
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</table> }} |
Revision as of 18:36, 1 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11n195's Link Presentations]
Planar diagram presentation | X8192 X2,11,3,12 X12,3,13,4 X16,5,17,6 X6718 X4,15,5,16 X20,14,21,13 X9,18,10,19 X19,10,20,11 X22,18,7,17 X14,22,15,21 |
Gauss code | {1, -2, 3, -6, 4, -5}, {5, -1, -8, 9, 2, -3, 7, -11, 6, -4, 10, 8, -9, -7, 11, -10} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -3 (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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