L9n28
From Knot Atlas
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![]() (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
L9n28 is in the Rolfsen table of links. |
Link Presentations
[edit Notes on L9n28's Link Presentations]
Planar diagram presentation | X6172 X12,7,13,8 X4,13,1,14 X18,10,15,9 X8493 X5,17,6,16 X17,5,18,14 X10,16,11,15 X2,12,3,11 |
Gauss code | {1, -9, 5, -3}, {8, 6, -7, -4}, {-6, -1, 2, -5, 4, -8, 9, -2, 3, 7} |
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 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{(u-1) (w-1)^2 (v w+1)}{\sqrt{u} \sqrt{v} w^{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 3 q^5-4 q^4+6 q^3-5 q^2+6 q-4+3 q^{-1} - q^{-2} } (db) |
Signature | 2 (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^6 a^{-2} +4 z^4 a^{-2} -z^4 a^{-4} -z^4+5 z^2 a^{-2} -3 z^2 a^{-4} -2 z^2+3 a^{-2} -4 a^{-4} + a^{-6} + a^{-2} z^{-2} -2 a^{-4} z^{-2} + a^{-6} z^{-2} } (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 2 z^7 a^{-1} +2 z^7 a^{-3} +8 z^6 a^{-2} +5 z^6 a^{-4} +3 z^6+a z^5-z^5 a^{-1} +z^5 a^{-3} +3 z^5 a^{-5} -21 z^4 a^{-2} -13 z^4 a^{-4} -8 z^4-2 a z^3-7 z^3 a^{-1} -8 z^3 a^{-3} -3 z^3 a^{-5} +17 z^2 a^{-2} +18 z^2 a^{-4} +6 z^2 a^{-6} +5 z^2+a z+3 z a^{-1} +7 z a^{-3} +5 z a^{-5} -7 a^{-2} -10 a^{-4} -5 a^{-6} -1-2 a^{-3} z^{-1} -2 a^{-5} z^{-1} + a^{-2} z^{-2} +2 a^{-4} z^{-2} + a^{-6} 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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