L11a72
From Knot Atlas
Jump to navigationJump to search
|
|
![]() (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a72's Link Presentations]
Planar diagram presentation | X6172 X12,3,13,4 X20,13,21,14 X16,7,17,8 X18,9,19,10 X8,17,9,18 X10,19,11,20 X22,15,5,16 X14,21,15,22 X2536 X4,11,1,12 |
Gauss code | {1, -10, 2, -11}, {10, -1, 4, -6, 5, -7, 11, -2, 3, -9, 8, -4, 6, -5, 7, -3, 9, -8} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation | ![]() |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -7 (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^{18} z^4-2 a^{18} z^2+a^{18}+2 a^{17} z^5-2 a^{17} z^3+3 a^{16} z^6-2 a^{16} z^4+4 a^{15} z^7-5 a^{15} z^5+4 a^{15} z^3+4 a^{14} z^8-6 a^{14} z^6+4 a^{14} z^4+a^{14} z^2+3 a^{13} z^9-5 a^{13} z^7+6 a^{13} z^5-11 a^{13} z^3+11 a^{13} z-3 a^{13} z^{-1} +a^{12} z^{10}+4 a^{12} z^8-20 a^{12} z^6+30 a^{12} z^4-24 a^{12} z^2+7 a^{12}+6 a^{11} z^9-24 a^{11} z^7+44 a^{11} z^5-53 a^{11} z^3+30 a^{11} z-7 a^{11} z^{-1} +a^{10} z^{10}+2 a^{10} z^8-19 a^{10} z^6+31 a^{10} z^4-24 a^{10} z^2+7 a^{10}+3 a^9 z^9-14 a^9 z^7+26 a^9 z^5-29 a^9 z^3+17 a^9 z-4 a^9 z^{-1} +2 a^8 z^8-8 a^8 z^6+8 a^8 z^4-a^8 z^2+a^7 z^7-5 a^7 z^5+7 a^7 z^3-2 a^7 z} (db) |
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). |
|
Integral Khovanov Homology
(db, data source) |
|
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. |
|