L11a327
From Knot Atlas
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a327's Link Presentations]
Planar diagram presentation | X10,1,11,2 X2,11,3,12 X12,3,13,4 X18,10,19,9 X6,13,7,14 X14,7,15,8 X8,15,1,16 X22,18,9,17 X16,22,17,21 X4,20,5,19 X20,6,21,5 |
Gauss code | {1, -2, 3, -10, 11, -5, 6, -7}, {4, -1, 2, -3, 5, -6, 7, -9, 8, -4, 10, -11, 9, -8} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -1 (db) |
HOMFLY-PT polynomial | (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^7 z^5-3 a^7 z^3+2 a^7 z+2 a^6 z^6-4 a^6 z^4+a^6 z^2+3 a^5 z^7-5 a^5 z^5+2 a^5 z^3-a^5 z+4 a^4 z^8-10 a^4 z^6+z^6 a^{-4} +14 a^4 z^4-4 z^4 a^{-4} -7 a^4 z^2+4 z^2 a^{-4} +3 a^3 z^9-6 a^3 z^7+2 z^7 a^{-3} +10 a^3 z^5-6 z^5 a^{-3} -10 a^3 z^3+4 z^3 a^{-3} +9 a^3 z-2 a^3 z^{-1} +a^2 z^{10}+4 a^2 z^8+3 z^8 a^{-2} -17 a^2 z^6-9 z^6 a^{-2} +30 a^2 z^4+10 z^4 a^{-2} -18 a^2 z^2-7 z^2 a^{-2} +3 a^2+ a^{-2} +6 a z^9+3 z^9 a^{-1} -21 a z^7-10 z^7 a^{-1} +43 a z^5+21 z^5 a^{-1} -47 a z^3-28 z^3 a^{-1} +24 a z+12 z a^{-1} -3 a z^{-1} - a^{-1} z^{-1} +z^{10}+3 z^8-15 z^6+26 z^4-21 z^2+3} (db) |
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , 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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