L9n13
From Knot Atlas
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![]() (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
L9n13 is in the Rolfsen table of links. |
Link Presentations
[edit Notes on L9n13's Link Presentations]
Planar diagram presentation | X8192 X11,17,12,16 X3,10,4,11 X15,3,16,2 X5,13,6,12 X6718 X9,14,10,15 X13,18,14,7 X17,4,18,5 |
Gauss code | {1, 4, -3, 9, -5, -6}, {6, -1, -7, 3, -2, 5, -8, 7, -4, 2, -9, 8} |
A Braid Representative |
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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 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(2) t(1)-t(1)+1) (t(1) t(2)-t(2)+1)}{t(1) t(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}}-\frac{4}{q^{5/2}}+\frac{2}{q^{3/2}}-\frac{1}{q^{13/2}}+\frac{2}{q^{11/2}}+\sqrt{q}-\frac{3}{\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 z^3 a^5+2 z a^5-z^5 a^3-4 z^3 a^3-4 z a^3+a^3 z^{-1} +z^3 a+z a-a z^{-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 -z^5 a^7+3 z^3 a^7-z a^7-2 z^6 a^6+7 z^4 a^6-5 z^2 a^6-z^7 a^5+2 z^5 a^5+z a^5-3 z^6 a^4+9 z^4 a^4-7 z^2 a^4-z^7 a^3+3 z^5 a^3-6 z^3 a^3+4 z a^3+a^3 z^{-1} -z^6 a^2+2 z^4 a^2-3 z^2 a^2-a^2-3 z^3 a+2 z a+a z^{-1} -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 (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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