L11a399
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 L11a399's Link Presentations]
Planar diagram presentation | X6172 X12,6,13,5 X8493 X2,14,3,13 X14,7,15,8 X4,15,1,16 X18,22,19,21 X20,9,21,10 X10,19,5,20 X16,12,17,11 X22,18,11,17 |
Gauss code | {1, -4, 3, -6}, {2, -1, 5, -3, 8, -9}, {10, -2, 4, -5, 6, -10, 11, -7, 9, -8, 7, -11} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation |
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{2 (t(1)-1) (t(2)-1)^2 (t(3)-1)^2}{\sqrt{t(1)} t(2) t(3)}} (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^6-4 q^5- q^{-5} +8 q^4+4 q^{-4} -13 q^3-7 q^{-3} +18 q^2+14 q^{-2} -20 q-17 q^{-1} +21} (db) |
Signature | 0 (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 z^6 a^{-6} -2 z^4 a^{-6} +4 z^7 a^{-5} +a^5 z^5-10 z^5 a^{-5} -a^5 z^3+5 z^3 a^{-5} +7 z^8 a^{-4} +4 a^4 z^6-19 z^6 a^{-4} -7 a^4 z^4+15 z^4 a^{-4} +4 a^4 z^2-4 z^2 a^{-4} -a^4 z^{-2} +a^4+6 z^9 a^{-3} +6 a^3 z^7-11 z^7 a^{-3} -7 a^3 z^5+2 z^5 a^{-3} +a^3 z^3+3 z^3 a^{-3} -a^3 z+2 a^3 z^{-1} +2 z^{10} a^{-2} +6 a^2 z^8+9 z^8 a^{-2} -a^2 z^6-32 z^6 a^{-2} -12 a^2 z^4+30 z^4 a^{-2} +8 a^2 z^2-8 z^2 a^{-2} -2 a^2 z^{-2} +a^2+5 a z^9+11 z^9 a^{-1} -a z^7-22 z^7 a^{-1} -3 a z^5+17 z^5 a^{-1} -2 a z^3-6 z^3 a^{-1} -a z+2 a z^{-1} +2 z^{10}+8 z^8-17 z^6+8 z^4- 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} ). |
|
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. |
|