L11a229: Difference between revisions
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k = 229 | |
k = 229 | |
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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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braid_table = <table cellspacing=0 cellpadding=0 border=0> |
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<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]]</td></tr> |
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</table> | |
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khovanov_table = <table border=1> |
khovanov_table = <table border=1> |
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<tr align=center> |
<tr align=center> |
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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> |
</tr> |
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<tr valign=top><td colspan=2>Loading KnotTheory` (version of |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 2, 2005, 15:8:39)...</td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Link[11, Alternating, 229]]</nowiki></pre></td></tr> |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Link[11, Alternating, 229]]</nowiki></pre></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> |
<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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{5, -1, 8, -9, 2, -3, 7, -11, 6, -4, 10, -8, 9, -7, 11, -10}]</nowiki></pre></td></tr> |
{5, -1, 8, -9, 2, -3, 7, -11, 6, -4, 10, -8, 9, -7, 11, -10}]</nowiki></pre></td></tr> |
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<tr |
<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>BR[Link[11, Alternating, 229]]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[3, {1, -2, -2, 1, 1, -2, -2, 1, -2, -2, 1}]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Link[11, Alternating, 229]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a229_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[7]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki> |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>KnotSignature[Link[11, Alternating, 229]]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>-1</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>J=Jones[Link[11, Alternating, 229]][q]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -(13/2) 3 8 13 18 20 21 |
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-q + ----- - ---- + ---- - ---- + ---- - ------- + 17 Sqrt[q] - |
-q + ----- - ---- + ---- - ---- + ---- - ------- + 17 Sqrt[q] - |
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11/2 9/2 7/2 5/2 3/2 Sqrt[q] |
11/2 9/2 7/2 5/2 3/2 Sqrt[q] |
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Line 70: | Line 77: | ||
3/2 5/2 7/2 9/2 |
3/2 5/2 7/2 9/2 |
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13 q + 8 q - 3 q + q</nowiki></pre></td></tr> |
13 q + 8 q - 3 q + q</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[ |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Link[11, Alternating, 229]][q]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[ |
<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> -18 -16 4 -12 3 3 2 6 3 2 4 |
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5 + q - q + --- - q + --- + -- - -- + -- - -- - q - 2 q + |
5 + q - q + --- - q + --- + -- - -- + -- - -- - q - 2 q + |
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14 10 8 6 4 2 |
14 10 8 6 4 2 |
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6 8 10 12 |
6 8 10 12 |
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q - 4 q + q - q</nowiki></pre></td></tr> |
q - 4 q + q - q</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[ |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Link[11, Alternating, 229]][a, z]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[ |
<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> 3 3 |
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2 5 a 3 a 9 z 3 10 z 3 3 3 |
2 5 a 3 a 9 z 3 10 z 3 3 3 |
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--- - --- + ---- + --- - 21 a z + 9 a z + ----- - 29 a z + 10 a z + |
--- - --- + ---- + --- - 21 a z + 9 a z + ----- - 29 a z + 10 a z + |
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---- - 20 a z + 5 a z + -- - 7 a z + a z - a z |
---- - 20 a z + 5 a z + -- - 7 a z + a z - a z |
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a a</nowiki></pre></td></tr> |
a a</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[ |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Link[11, Alternating, 229]][a, z]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[ |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 |
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-4 2 2 5 a 3 a 9 z 3 5 |
-4 2 2 5 a 3 a 9 z 3 5 |
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-5 + a - 5 a + --- + --- + ---- - --- - 25 a z - 12 a z + 3 a z - |
-5 + a - 5 a + --- + --- + ---- - --- - 25 a z - 12 a z + 3 a z - |
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7 a z - ---- - 11 a z - 6 a z - 2 z - 2 a z |
7 a z - ---- - 11 a z - 6 a z - 2 z - 2 a z |
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a</nowiki></pre></td></tr> |
a</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[ |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Link[11, Alternating, 229]][q, t]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[ |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 11 1 1 3 5 3 8 5 |
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11 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
11 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
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2 14 6 12 6 12 5 10 4 8 4 8 3 6 3 |
2 14 6 12 6 12 5 10 4 8 4 8 3 6 3 |
Revision as of 19:16, 2 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a229'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 X18,10,19,9 X10,20,11,19 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 | ||||
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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