L10a63
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L10a63's Link Presentations]
Planar diagram presentation | X8192 X10,4,11,3 X20,10,7,9 X2738 X4,20,5,19 X14,5,15,6 X16,11,17,12 X18,13,19,14 X12,17,13,18 X6,15,1,16 |
Gauss code | {1, -4, 2, -5, 6, -10}, {4, -1, 3, -2, 7, -9, 8, -6, 10, -7, 9, -8, 5, -3} |
A Braid Representative | |||||
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in 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 u} , 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 v} , 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 w} , ...) | 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 -\frac{u^2 v^4-2 u^2 v^3+2 u^2 v^2-2 u^2 v+u^2-2 u v^4+5 u v^3-5 u v^2+5 u v-2 u+v^4-2 v^3+2 v^2-2 v+1}{u v^2}} (db) |
Jones polynomial | (db) |
Signature | -3 (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 -z^4 a^{10}+z^2 a^{10}-3 z^5 a^9+3 z^3 a^9-5 z^6 a^8+6 z^4 a^8-3 z^2 a^8+a^8-6 z^7 a^7+10 z^5 a^7-10 z^3 a^7+5 z a^7-a^7 z^{-1} -4 z^8 a^6+2 z^6 a^6+6 z^4 a^6-9 z^2 a^6+3 a^6-z^9 a^5-10 z^7 a^5+32 z^5 a^5-35 z^3 a^5+16 z a^5-3 a^5 z^{-1} -7 z^8 a^4+14 z^6 a^4-3 z^4 a^4-6 z^2 a^4+3 a^4-z^9 a^3-7 z^7 a^3+29 z^5 a^3-32 z^3 a^3+15 z a^3-2 a^3 z^{-1} -3 z^8 a^2+6 z^6 a^2+z^4 a^2-3 z^2 a^2-3 z^7 a+10 z^5 a-10 z^3 a+4 z a-z^6+3 z^4-2 z^2} (db) |
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums 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 \chi} (fixed , alternation over 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 r} ). |
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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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