L11a378

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L11a377.gif

L11a377

L11a379.gif

L11a379

L11a378.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

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Link Presentations

[edit Notes on L11a378's Link Presentations]

Planar diagram presentation X12,1,13,2 X2,13,3,14 X14,3,15,4 X4,11,5,12 X16,8,17,7 X18,6,19,5 X22,16,11,15 X6,18,7,17 X8,22,9,21 X20,10,21,9 X10,20,1,19
Gauss code {1, -2, 3, -4, 6, -8, 5, -9, 10, -11}, {4, -1, 2, -3, 7, -5, 8, -6, 11, -10, 9, -7}
A Braid Representative
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A Morse Link Presentation L11a378 ML.gif

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 ).   
\ r
  \  
j \
-4-3-2-101234567χ
14           1-1
12          1 1
10         31 -2
8        51  4
6       43   -1
4      85    3
2     55     0
0    67      -1
-2   46       2
-4  25        -3
-6 14         3
-8 2          -2
-101           1
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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L11a377

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L11a379