L11n262
From Knot Atlas
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 (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11n262's Link Presentations]
| Planar diagram presentation | X6172 X10,3,11,4 X14,7,15,8 X8,13,5,14 X11,18,12,19 X19,22,20,9 X15,20,16,21 X21,16,22,17 X17,12,18,13 X2536 X4,9,1,10 |
| Gauss code | {1, -10, 2, -11}, {10, -1, 3, -4}, {11, -2, -5, 9, 4, -3, -7, 8, -9, 5, -6, 7, -8, 6} |
| 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 w^3-u v w+u v+u w^3-3 u w^2+3 u w-u+v w^3-3 v w^2+3 v w-v-w^3+w^2-1}{\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 - q^{-13} +2 q^{-12} -5 q^{-11} +6 q^{-10} -6 q^{-9} +7 q^{-8} -4 q^{-7} +5 q^{-6} - q^{-5} + q^{-3} } (db) |
| Signature | -4 (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^{14} z^{-2} +3 a^{12} z^{-2} +4 a^{12}-5 z^2 a^{10}-2 a^{10} z^{-2} -7 a^{10}+z^4 a^8-a^8 z^{-2} -a^8+z^6 a^6+6 z^4 a^6+8 z^2 a^6+a^6 z^{-2} +4 a^6} (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^{15} z^7-5 a^{15} z^5+9 a^{15} z^3-7 a^{15} z+2 a^{15} z^{-1} +2 a^{14} z^8-8 a^{14} z^6+8 a^{14} z^4-2 a^{14} z^2-a^{14} z^{-2} +a^{14}+a^{13} z^9+2 a^{13} z^7-24 a^{13} z^5+39 a^{13} z^3-27 a^{13} z+8 a^{13} z^{-1} +6 a^{12} z^8-24 a^{12} z^6+24 a^{12} z^4-10 a^{12} z^2-3 a^{12} z^{-2} +5 a^{12}+a^{11} z^9+4 a^{11} z^7-33 a^{11} z^5+52 a^{11} z^3-34 a^{11} z+10 a^{11} z^{-1} +4 a^{10} z^8-18 a^{10} z^6+24 a^{10} z^4-13 a^{10} z^2-2 a^{10} z^{-2} +4 a^{10}+3 a^9 z^7-15 a^9 z^5+22 a^9 z^3-10 a^9 z+2 a^9 z^{-1} -a^8 z^6+2 a^8 z^4+3 a^8 z^2+a^8 z^{-2} -3 a^8-a^7 z^5+4 a^7 z-2 a^7 z^{-1} +a^6 z^6-6 a^6 z^4+8 a^6 z^2+a^6 z^{-2} -4 a^6} (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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