L9n10
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
L9n10 is 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 9^2_{58}} in the Rolfsen table of links. |
Link Presentations
[edit Notes on L9n10's Link Presentations]
Planar diagram presentation | X6172 X10,3,11,4 X7,14,8,15 X18,16,5,15 X16,12,17,11 X12,18,13,17 X13,8,14,9 X2536 X4,9,1,10 |
Gauss code | {1, -8, 2, -9}, {8, -1, -3, 7, 9, -2, 5, -6, -7, 3, 4, -5, 6, -4} |
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{t(1) t(2)^3-t(2)^3-2 t(1) t(2)^2+3 t(2)^2+3 t(1) t(2)-2 t(2)-t(1)+1}{\sqrt{t(1)} t(2)^{3/2}}} (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 -\frac{2}{q^{9/2}}+\frac{3}{q^{7/2}}+q^{5/2}-\frac{5}{q^{5/2}}-3 q^{3/2}+\frac{5}{q^{3/2}}+4 \sqrt{q}-\frac{5}{\sqrt{q}}} (db) |
Signature | -1 (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 a^5 z^{-1} +z^3 a^3-a^3 z^{-1} -z^5 a-3 z^3 a-3 z a+z^3 a^{-1} +z a^{-1} } (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 3 a^5 z^3-4 a^5 z+a^5 z^{-1} +a^4 z^6+a^4 z^2-a^4+a^3 z^7+2 a^3 z^3-3 a^3 z+a^3 z^{-1} +4 a^2 z^6-5 a^2 z^4+z^4 a^{-2} +2 a^2 z^2-z^2 a^{-2} +a z^7+3 a z^5+3 z^5 a^{-1} -6 a z^3-5 z^3 a^{-1} +2 a z+z a^{-1} +3 z^6-4 z^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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