L9a55
From Knot Atlas
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![]() (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
L9a55 is in the Rolfsen table of links. |
Link Presentations
[edit Notes on L9a55's Link Presentations]
Planar diagram presentation | X6172 X2536 X16,12,17,11 X10,3,11,4 X4,9,1,10 X14,7,15,8 X8,13,5,14 X18,16,13,15 X12,18,9,17 |
Gauss code | {1, -2, 4, -5}, {2, -1, 6, -7}, {5, -4, 3, -9}, {7, -6, 8, -3, 9, -8} |
A Braid Representative |
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A Morse Link Presentation | ![]() |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (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^7 z^{-1} +a^7 z^{-3} -3 z a^5-5 a^5 z^{-1} -3 a^5 z^{-3} +3 z^3 a^3+6 z a^3+7 a^3 z^{-1} +3 a^3 z^{-3} -z^5 a-2 z^3 a-3 z a-3 a z^{-1} -a z^{-3} +z^3 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 -a^4 z^8-a^2 z^8-a^5 z^7-5 a^3 z^7-4 a z^7-a^6 z^6-a^4 z^6-6 a^2 z^6-6 z^6-a^7 z^5-3 a^5 z^5+4 a^3 z^5+2 a z^5-4 z^5 a^{-1} -2 a^4 z^4+7 a^2 z^4-z^4 a^{-2} +8 z^4+4 a^7 z^3+12 a^5 z^3+8 a^3 z^3+4 a z^3+4 z^3 a^{-1} +6 a^6 z^2+12 a^4 z^2+6 a^2 z^2-6 a^7 z-14 a^5 z-14 a^3 z-6 a z-8 a^6-15 a^4-8 a^2+4 a^7 z^{-1} +9 a^5 z^{-1} +9 a^3 z^{-1} +4 a z^{-1} +3 a^6 z^{-2} +6 a^4 z^{-2} +3 a^2 z^{-2} -a^7 z^{-3} -3 a^5 z^{-3} -3 a^3 z^{-3} -a z^{-3} } (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 ). |
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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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