L11n268
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11n268's Link Presentations]
Planar diagram presentation | X6172 X3,11,4,10 X7,17,8,16 X15,5,16,8 X11,19,12,18 X17,9,18,22 X13,21,14,20 X19,13,20,12 X21,15,22,14 X2536 X9,1,10,4 |
Gauss code | {1, -10, -2, 11}, {10, -1, -3, 4}, {-11, 2, -5, 8, -7, 9, -4, 3, -6, 5, -8, 7, -9, 6} |
A Braid Representative | {{{braid_table}}} |
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{t(3)^5+t(1) t(3)^4-2 t(1) t(2) t(3)^4+t(2) t(3)^4-2 t(3)^4-t(1) t(3)^3+2 t(1) t(2) t(3)^3-t(2) t(3)^3+2 t(3)^3+t(1) t(3)^2-2 t(1) t(2) t(3)^2+t(2) t(3)^2-2 t(3)^2-t(1) t(3)+2 t(1) t(2) t(3)-t(2) t(3)+2 t(3)-t(1) t(2)}{\sqrt{t(1)} \sqrt{t(2)} t(3)^{5/2}}} (db) |
Jones 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 -q^{11}+2 q^{10}-5 q^9+6 q^8-8 q^7+10 q^6-7 q^5+7 q^4-3 q^3+3 q^2} (db) |
Signature | 4 (db) |
HOMFLY-PT 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^2 a^{-10} -2 a^{-10} z^{-2} -3 a^{-10} +3 z^4 a^{-8} +12 z^2 a^{-8} +7 a^{-8} z^{-2} +15 a^{-8} -2 z^6 a^{-6} -11 z^4 a^{-6} -23 z^2 a^{-6} -8 a^{-6} z^{-2} -22 a^{-6} +3 z^4 a^{-4} +11 z^2 a^{-4} +3 a^{-4} z^{-2} +10 a^{-4} } (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^5 a^{-13} -3 z^3 a^{-13} +3 z a^{-13} - a^{-13} z^{-1} +2 z^6 a^{-12} -4 z^4 a^{-12} + a^{-12} +2 z^7 a^{-11} -z^5 a^{-11} -6 z^3 a^{-11} +3 z a^{-11} - a^{-11} z^{-1} +2 z^8 a^{-10} -3 z^6 a^{-10} +4 z^4 a^{-10} -9 z^2 a^{-10} -2 a^{-10} z^{-2} +7 a^{-10} +z^9 a^{-9} +2 z^7 a^{-9} -13 z^5 a^{-9} +26 z^3 a^{-9} -21 z a^{-9} +7 a^{-9} z^{-1} +6 z^8 a^{-8} -24 z^6 a^{-8} +44 z^4 a^{-8} -36 z^2 a^{-8} -7 a^{-8} z^{-2} +22 a^{-8} +z^9 a^{-7} +3 z^7 a^{-7} -23 z^5 a^{-7} +52 z^3 a^{-7} -45 z a^{-7} +15 a^{-7} z^{-1} +4 z^8 a^{-6} -19 z^6 a^{-6} +42 z^4 a^{-6} -46 z^2 a^{-6} -8 a^{-6} z^{-2} +28 a^{-6} +3 z^7 a^{-5} -12 z^5 a^{-5} +23 z^3 a^{-5} -24 z a^{-5} +8 a^{-5} z^{-1} +6 z^4 a^{-4} -19 z^2 a^{-4} -3 a^{-4} z^{-2} +13 a^{-4} } (db) |
Khovanov Homology
The coefficients of the monomials 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 t^rq^j} 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 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 j} , 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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