L11a388
From Knot Atlas
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 (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a388's Link Presentations]
| Planar diagram presentation | X6172 X10,3,11,4 X14,7,15,8 X8,13,5,14 X18,11,19,12 X22,15,9,16 X20,17,21,18 X16,21,17,22 X12,19,13,20 X2536 X4,9,1,10 |
| Gauss code | {1, -10, 2, -11}, {10, -1, 3, -4}, {11, -2, 5, -9, 4, -3, 6, -8, 7, -5, 9, -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{3 u v w^2-4 u v w+2 u v+2 u w^3-6 u w^2+6 u w-2 u+2 v w^3-6 v w^2+6 v w-2 v-2 w^3+4 w^2-3 w}{\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^{-2} -3 q^{-3} +7 q^{-4} -10 q^{-5} +16 q^{-6} -15 q^{-7} +16 q^{-8} -13 q^{-9} +10 q^{-10} -6 q^{-11} +2 q^{-12} - q^{-13} } (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}-6 a^{10} z^2-2 a^{10} z^{-2} -7 a^{10}+3 a^8 z^4+3 a^8 z^2-a^8 z^{-2} -a^8+3 a^6 z^4+5 a^6 z^2+a^6 z^{-2} +4 a^6+a^4 z^4+a^4 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 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^8-7 a^{14} z^6+7 a^{14} z^4-2 a^{14} z^2-a^{14} z^{-2} +a^{14}+2 a^{13} z^9-a^{13} z^7-18 a^{13} z^5+36 a^{13} z^3-27 a^{13} z+8 a^{13} z^{-1} +a^{12} z^{10}+5 a^{12} z^8-22 a^{12} z^6+19 a^{12} z^4-7 a^{12} z^2-3 a^{12} z^{-2} +5 a^{12}+6 a^{11} z^9-6 a^{11} z^7-27 a^{11} z^5+49 a^{11} z^3-34 a^{11} z+10 a^{11} z^{-1} +a^{10} z^{10}+10 a^{10} z^8-28 a^{10} z^6+17 a^{10} z^4-5 a^{10} z^2-2 a^{10} z^{-2} +4 a^{10}+4 a^9 z^9+3 a^9 z^7-23 a^9 z^5+23 a^9 z^3-10 a^9 z+2 a^9 z^{-1} +7 a^8 z^8-7 a^8 z^6-4 a^8 z^4+9 a^8 z^2+a^8 z^{-2} -3 a^8+7 a^7 z^7-6 a^7 z^5-a^7 z^3+4 a^7 z-2 a^7 z^{-1} +6 a^6 z^6-8 a^6 z^4+8 a^6 z^2+a^6 z^{-2} -4 a^6+3 a^5 z^5-2 a^5 z^3+a^4 z^4-a^4 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 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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