L11n458

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L11n457.gif

L11n457

L11n459.gif

L11n459

L11n458.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

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Link L11n458.
A graph, L11n458.
A part of a knot and a part of a graph.

Link Presentations

[edit Notes on L11n458's Link Presentations]

Planar diagram presentation X6172 X3,13,4,12 X7,21,8,20 X19,5,20,10 X13,19,14,22 X21,11,22,18 X17,15,18,14 X9,17,10,16 X15,9,16,8 X2536 X11,1,12,4
Gauss code {1, -10, -2, 11}, {-4, 3, -6, 5}, {10, -1, -3, 9, -8, 4}, {-11, 2, -5, 7, -9, 8, -7, 6}
A Braid Representative
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A Morse Link Presentation L11n458 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 3 (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 ).   
\ r
  \  
j \
0123456789χ
22         1-1
20        3 3
18       41 -3
16      73  4
14     76   -1
12    85    3
10   59     4
8  66      0
6 17       6
424        -2
23         3
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).

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L11n457.gif

L11n457

L11n459.gif

L11n459