L10a6: Difference between revisions
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Revision as of 13:14, 30 August 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L10a6's Link Presentations]
Planar diagram presentation | X6172 X18,7,19,8 X4,19,1,20 X12,6,13,5 X8493 X16,13,17,14 X14,9,15,10 X10,15,11,16 X20,12,5,11 X2,18,3,17 |
Gauss code | {1, -10, 5, -3}, {4, -1, 2, -5, 7, -8, 9, -4, 6, -7, 8, -6, 10, -2, 3, -9} |
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 \frac{(u-1) (v-1) \left(v^4-3 v^3+5 v^2-3 v+1\right)}{\sqrt{u} v^{5/2}}} (db) |
Jones polynomial | (db) |
Signature | -1 (db) |
HOMFLY-PT polynomial | (db) |
Kauffman polynomial | (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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