L9n20
From Knot Atlas
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![]() (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
L9n20 is in the Rolfsen table of links. |
Link Presentations
[edit Notes on L9n20's Link Presentations]
Planar diagram presentation | X6172 X3,11,4,10 X7,15,8,14 X13,5,14,8 X11,17,12,16 X15,9,16,18 X17,13,18,12 X2536 X9,1,10,4 |
Gauss code | {1, -8, -2, 9}, {8, -1, -3, 4}, {-9, 2, -5, 7, -4, 3, -6, 5, -7, 6} |
A Braid Representative |
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A Morse Link Presentation | ![]() |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | 2 (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^7 a^{-5} +z^7 a^{-7} +4 z^6 a^{-4} +6 z^6 a^{-6} +2 z^6 a^{-8} +3 z^5 a^{-3} +5 z^5 a^{-5} +3 z^5 a^{-7} +z^5 a^{-9} -11 z^4 a^{-4} -16 z^4 a^{-6} -5 z^4 a^{-8} -6 z^3 a^{-3} -18 z^3 a^{-5} -15 z^3 a^{-7} -3 z^3 a^{-9} +6 z^2 a^{-2} +18 z^2 a^{-4} +15 z^2 a^{-6} +3 z^2 a^{-8} +11 z a^{-3} +21 z a^{-5} +13 z a^{-7} +3 z a^{-9} -7 a^{-2} -14 a^{-4} -10 a^{-6} -2 a^{-8} -5 a^{-3} z^{-1} -9 a^{-5} z^{-1} -5 a^{-7} z^{-1} - a^{-9} z^{-1} +2 a^{-2} z^{-2} +5 a^{-4} z^{-2} +4 a^{-6} z^{-2} + a^{-8} z^{-2} } (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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