L10a55: Difference between revisions
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k = 55 | |
k = 55 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-10,8,-6:4,-1,2,-3,7,-8,5,-4,9,-5,6,-7,10,-9/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-10,8,-6:4,-1,2,-3,7,-8,5,-4,9,-5,6,-7,10,-9/goTop.html | |
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braid_table = <table cellspacing=0 cellpadding=0 border=0> |
braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre"> |
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<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr> |
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr> |
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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 September |
<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[10, Alternating, 55]]</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[10, Alternating, 55]]</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>10</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>10</nowiki></pre></td></tr> |
Latest revision as of 03:59, 3 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L10a55's Link Presentations]
Planar diagram presentation | X8192 X2,9,3,10 X10,3,11,4 X14,8,15,7 X16,13,17,14 X6,18,1,17 X18,12,19,11 X12,6,13,5 X20,16,7,15 X4,19,5,20 |
Gauss code | {1, -2, 3, -10, 8, -6}, {4, -1, 2, -3, 7, -8, 5, -4, 9, -5, 6, -7, 10, -9} |
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 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2 a z^9-2 z^9 a^{-1} -6 a^2 z^8-4 z^8 a^{-2} -10 z^8-8 a^3 z^7-8 a z^7-3 z^7 a^{-1} -3 z^7 a^{-3} -7 a^4 z^6+5 a^2 z^6+10 z^6 a^{-2} -z^6 a^{-4} +23 z^6-4 a^5 z^5+9 a^3 z^5+23 a z^5+19 z^5 a^{-1} +9 z^5 a^{-3} -a^6 z^4+7 a^4 z^4+2 a^2 z^4-6 z^4 a^{-2} +3 z^4 a^{-4} -15 z^4+3 a^5 z^3-a^3 z^3-14 a z^3-18 z^3 a^{-1} -8 z^3 a^{-3} -a^4 z^2-a^2 z^2+z^2 a^{-2} -2 z^2 a^{-4} +3 z^2-2 a^3 z+5 z a^{-1} +3 z a^{-3} -a^2+a^3 z^{-1} +a z^{-1} } (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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