L11n204: Difference between revisions
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k = 204 | |
k = 204 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,-5,11,7,-8,-2,10:8,-1,-3,5,6,-7,-9,2,-10,3,4,-6,-11,9/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,-5,11,7,-8,-2,10:8,-1,-3,5,6,-7,-9,2,-10,3,4,-6,-11,9/goTop.html | |
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braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre"> |
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<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.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 3, 2005, 2:11:43)...</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, NonAlternating, 204]]</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, NonAlternating, 204]]</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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{8, -1, -3, 5, 6, -7, -9, 2, -10, 3, 4, -6, -11, 9}]</nowiki></pre></td></tr> |
{8, -1, -3, 5, 6, -7, -9, 2, -10, 3, 4, -6, -11, 9}]</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, NonAlternating, 204]]</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, -1, -2, -1, -1, -2, -1, -2, -1, -2}]</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, NonAlternating, 204]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11n204_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, NonAlternating, 204]]</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>-8</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, NonAlternating, 204]][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> -(23/2) -(21/2) -(13/2) -(9/2) |
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-q + q - q - q</nowiki></pre></td></tr> |
-q + 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[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Link[11, NonAlternating, 204]][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> -44 -38 -36 -30 -26 2 2 2 -18 -16 |
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-q + q + q - q + q + --- + --- + --- + q + q |
-q + q + q - q + q + --- + --- + --- + q + q |
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24 22 20 |
24 22 20 |
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q q q</nowiki></pre></td></tr> |
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, NonAlternating, 204]][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> 9 11 13 |
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-2 a 3 a a 9 11 13 9 3 |
-2 a 3 a a 9 11 13 9 3 |
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----- + ----- - --- - 18 a z + 17 a z - 3 a z - 36 a z + |
----- + ----- - --- - 18 a z + 17 a z - 3 a z - 36 a z + |
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11 3 13 3 9 5 11 5 9 7 11 7 9 9 |
11 3 13 3 9 5 11 5 9 7 11 7 9 9 |
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20 a z - a z - 28 a z + 8 a z - 9 a z + a z - a z</nowiki></pre></td></tr> |
20 a z - a z - 28 a z + 8 a z - 9 a z + a z - a z</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, NonAlternating, 204]][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> 9 11 13 |
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10 12 14 2 a 3 a a 9 11 |
10 12 14 2 a 3 a a 9 11 |
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-3 a - 3 a - a + ---- + ----- + --- - 18 a z - 20 a z - |
-3 a - 3 a - a + ---- + ----- + --- - 18 a z - 20 a z - |
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12 6 9 7 11 7 10 8 12 8 9 9 11 9 |
12 6 9 7 11 7 10 8 12 8 9 9 11 9 |
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8 a z + 9 a z + 9 a z - a z - a z - a z - a z</nowiki></pre></td></tr> |
8 a z + 9 a z + 9 a z - a z - a z - a z - a z</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, NonAlternating, 204]][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> -10 -8 1 1 1 1 1 1 |
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q + q + ------ + ------ + ------ + ------ + ------ + ------ + |
q + q + ------ + ------ + ------ + ------ + ------ + ------ + |
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24 8 22 8 22 7 18 6 20 5 18 5 |
24 8 22 8 22 7 18 6 20 5 18 5 |
Latest revision as of 03:41, 3 September 2005
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![]() (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11n204's Link Presentations]
Planar diagram presentation | X10,1,11,2 X7,16,8,17 X11,18,12,19 X2,19,3,20 X3,12,4,13 X20,13,21,14 X14,5,15,6 X6,9,7,10 X15,22,16,9 X17,8,18,1 X21,4,22,5 |
Gauss code | {1, -4, -5, 11, 7, -8, -2, 10}, {8, -1, -3, 5, 6, -7, -9, 2, -10, 3, 4, -6, -11, 9} |
A Braid Representative |
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A Morse Link Presentation | ![]() |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -8 (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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