L11a479: Difference between revisions
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n = 11 | |
n = 11 | |
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t = a | |
t = <nowiki>a</nowiki> | |
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k = 479 | |
k = 479 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:7,-3,9,-5,8,-4:10,-1,3,-6,5,-2,11,-9,6,-7,4,-8/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:7,-3,9,-5,8,-4:10,-1,3,-6,5,-2,11,-9,6,-7,4,-8/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, 479]]</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, 479]]]</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[10, 4, 11, 3], X[18, 7, 19, 8], X[22, 15, 17, 16], |
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X[20, 10, 21, 9], X[8, 13, 9, 14], X[14, 17, 15, 18], |
X[20, 10, 21, 9], X[8, 13, 9, 14], X[14, 17, 15, 18], |
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X[16, 21, 5, 22], X[12, 20, 13, 19], X[2, 5, 3, 6], X[4, 12, 1, 11]]</nowiki></ |
X[16, 21, 5, 22], X[12, 20, 13, 19], X[2, 5, 3, 6], X[4, 12, 1, 11]]</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, 3, -6, 5, -2, 11, -9, 6, -7, 4, -8}]</nowiki></ |
{10, -1, 3, -6, 5, -2, 11, -9, 6, -7, 4, -8}]</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, 479]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a479_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, 479]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:L11a479_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>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 + -- - -- + -- - -- + -- - -- - 14 q + 9 q - 4 q + q |
19 - q + -- - -- + -- - -- + -- - -- - 14 q + 9 q - 4 q + q |
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6 5 4 3 2 q |
6 5 4 3 2 q |
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q q q q q</nowiki></ |
q q q q 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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-1 - q + q - --- + --- + --- + q + -- + -- + -- + -- + 4 q - |
-1 - q + q - --- + --- + --- + q + -- + -- + -- + -- + 4 q - |
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16 14 12 8 6 4 2 |
16 14 12 8 6 4 2 |
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4 6 8 10 12 |
4 6 8 10 12 |
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4 q + 2 q + 2 q - 2 q + q</nowiki></ |
4 q + 2 q + 2 q - 2 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 2 4 6 -2 2 a a 2 z 4 2 |
-2 2 4 6 -2 2 a a 2 z 4 2 |
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-1 + a - a + 2 a - a + z - ---- + -- - 3 z + -- + 3 a z - |
-1 + a - a + 2 a - a + z - ---- + -- - 3 z + -- + 3 a z - |
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a z - 2 z + -- - a z + 2 a z - z - a z |
a z - 2 z + -- - a z + 2 a z - z - a z |
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2 |
2 |
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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 2 4 6 -2 2 a a 2 a 2 a z |
-2 2 4 6 -2 2 a a 2 a 2 a z |
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1 - a + 7 a + 9 a + 3 a - z - ---- - -- + --- + ---- - - - |
1 - a + 7 a + 9 a + 3 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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-- + 11 q + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
-- + 11 q + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
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q 15 7 13 6 11 6 11 5 9 5 9 4 7 4 |
q 15 7 13 6 11 6 11 5 9 5 9 4 7 4 |
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3 2 5 2 5 3 7 3 9 4 |
3 2 5 2 5 3 7 3 9 4 |
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3 q t + 6 q t + q t + 3 q t + q t</nowiki></ |
3 q t + 6 q t + q t + 3 q t + q t</nowiki></code></td></tr> |
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</table> }} |
Revision as of 17:41, 1 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a479's Link Presentations]
Planar diagram presentation | X6172 X10,4,11,3 X18,7,19,8 X22,15,17,16 X20,10,21,9 X8,13,9,14 X14,17,15,18 X16,21,5,22 X12,20,13,19 X2536 X4,12,1,11 |
Gauss code | {1, -10, 2, -11}, {7, -3, 9, -5, 8, -4}, {10, -1, 3, -6, 5, -2, 11, -9, 6, -7, 4, -8} |
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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