L11a463
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 (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a463's Link Presentations]
| Planar diagram presentation | X6172 X14,4,15,3 X8,14,9,13 X22,8,13,7 X20,15,21,16 X16,6,17,5 X18,12,19,11 X12,18,5,17 X10,20,11,19 X2,9,3,10 X4,22,1,21 |
| Gauss code | {1, -10, 2, -11}, {6, -1, 4, -3, 10, -9, 7, -8}, {3, -2, 5, -6, 8, -7, 9, -5, 11, -4} |
| A Braid Representative |
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| A Morse Link Presentation | 
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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{u v^3 w^2-2 u v^3 w+u v^2 w^3-3 u v^2 w^2+4 u v^2 w-2 u v^2-2 u v w^3+4 u v w^2-3 u v w+u v+u w^3-2 u w^2+u w-v^3 w^2+2 v^3 w-v^3-v^2 w^3+3 v^2 w^2-4 v^2 w+2 v^2+2 v w^3-4 v w^2+3 v w-v+2 w^2-w}{\sqrt{u} v^{3/2} 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 q^9-3 q^8+7 q^7-9 q^6+15 q^5-17 q^4+17 q^3-15 q^2+12 q-7+4 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} +z^6 a^{-4} +2 z^4 a^{-2} +2 z^4 a^{-4} -2 z^4 a^{-6} -z^4+z^2 a^{-2} +2 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} -z^2+ a^{-4} -3 a^{-6} + a^{-8} +1+ a^{-4} z^{-2} -2 a^{-6} z^{-2} + a^{-8} 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 z^6 a^{-10} -3 z^4 a^{-10} +z^2 a^{-10} +3 z^7 a^{-9} -8 z^5 a^{-9} +2 z^3 a^{-9} +6 z^8 a^{-8} -22 z^6 a^{-8} +28 z^4 a^{-8} -20 z^2 a^{-8} - a^{-8} z^{-2} +8 a^{-8} +5 z^9 a^{-7} -13 z^7 a^{-7} +5 z^5 a^{-7} +11 z^3 a^{-7} -11 z a^{-7} +2 a^{-7} z^{-1} +2 z^{10} a^{-6} +4 z^8 a^{-6} -30 z^6 a^{-6} +49 z^4 a^{-6} -31 z^2 a^{-6} -2 a^{-6} z^{-2} +13 a^{-6} +10 z^9 a^{-5} -30 z^7 a^{-5} +32 z^5 a^{-5} -11 z a^{-5} +2 a^{-5} z^{-1} +2 z^{10} a^{-4} +4 z^8 a^{-4} -18 z^6 a^{-4} +24 z^4 a^{-4} -12 z^2 a^{-4} - a^{-4} z^{-2} +5 a^{-4} +5 z^9 a^{-3} -8 z^7 a^{-3} +9 z^5 a^{-3} -7 z^3 a^{-3} +6 z^8 a^{-2} -7 z^6 a^{-2} -z^4 a^{-2} +6 z^7 a^{-1} +a z^5-9 z^5 a^{-1} -a z^3+z^3 a^{-1} +4 z^6-7 z^4+2 z^2+1} (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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