L8a8
From Knot Atlas
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
L8a8 is in the Rolfsen table of links, and the "seized Carrick bend" of practical knot-tying. |
Link Presentations
[edit Notes on L8a8's Link Presentations]
Planar diagram presentation | X8192 X10,4,11,3 X16,10,7,9 X2738 X14,12,15,11 X12,5,13,6 X4,13,5,14 X6,16,1,15 |
Gauss code | {1, -4, 2, -7, 6, -8}, {4, -1, 3, -2, 5, -6, 7, -5, 8, -3} |
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 | (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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