L11a410

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L11a409.gif

L11a409

L11a411.gif

L11a411

L11a410.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a410 at Knotilus!


Link Presentations

[edit Notes on L11a410's Link Presentations]

Planar diagram presentation X6172 X12,4,13,3 X20,16,21,15 X14,8,15,7 X10,12,5,11 X22,18,11,17 X16,22,17,21 X8,19,9,20 X18,9,19,10 X2536 X4,14,1,13
Gauss code {1, -10, 2, -11}, {10, -1, 4, -8, 9, -5}, {5, -2, 11, -4, 3, -7, 6, -9, 8, -3, 7, -6}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart1.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart2.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L11a410 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 4 (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
19           1-1
17          2 2
15         41 -3
13        52  3
11       74   -3
9      65    1
7     78     1
5    55      0
3   49       5
1  23        -1
-1 15         4
-3 1          -1
-51           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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L11a409.gif

L11a409

L11a411.gif

L11a411