L11n26
From Knot Atlas
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11n26's Link Presentations]
Planar diagram presentation | X6172 X16,7,17,8 X4,17,1,18 X5,12,6,13 X3849 X13,22,14,5 X21,14,22,15 X11,18,12,19 X9,20,10,21 X19,10,20,11 X15,2,16,3 |
Gauss code | {1, 11, -5, -3}, {-4, -1, 2, 5, -9, 10, -8, 4, -6, 7, -11, -2, 3, 8, -10, 9, -7, 6} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -5 (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 a^{14} z^4-4 a^{14} z^2+4 a^{14}+a^{13} z^5-a^{13} z^3-a^{13} z-a^{13} z^{-1} +a^{12} z^8-6 a^{12} z^6+18 a^{12} z^4-21 a^{12} z^2+9 a^{12}+a^{11} z^9-5 a^{11} z^7+11 a^{11} z^5-4 a^{11} z^3-3 a^{11} z-a^{11} z^{-1} +3 a^{10} z^8-13 a^{10} z^6+24 a^{10} z^4-14 a^{10} z^2+4 a^{10}+a^9 z^9-2 a^9 z^7-a^9 z^5+11 a^9 z^3-10 a^9 z+2 a^9 z^{-1} +2 a^8 z^8-5 a^8 z^6+2 a^8 z^4+4 a^8 z^2-2 a^8+3 a^7 z^7-10 a^7 z^5+11 a^7 z^3-7 a^7 z+2 a^7 z^{-1} +2 a^6 z^6-5 a^6 z^4+a^6 z^2+a^5 z^5-3 a^5 z^3+a^5 z} (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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