L11a459

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L11a458.gif

L11a458

L11a460.gif

L11a460

L11a459.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a459 at Knotilus!


Link Presentations

[edit Notes on L11a459's Link Presentations]

Planar diagram presentation X6172 X14,4,15,3 X16,5,17,6 X12,15,5,16 X22,20,13,19 X18,8,19,7 X10,14,11,13 X8,21,9,22 X20,9,21,10 X2,11,3,12 X4,18,1,17
Gauss code {1, -10, 2, -11}, {3, -1, 6, -8, 9, -7, 10, -4}, {7, -2, 4, -3, 11, -6, 5, -9, 8, -5}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L11a459 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 0 (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 \
-6-5-4-3-2-1012345χ
11           1-1
9          3 3
7         51 -4
5        83  5
3       105   -5
1      128    4
-1     1113     2
-3    89      -1
-5   511       6
-7  48        -4
-9 16         5
-11 3          -3
-131           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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L11a458.gif

L11a458

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L11a460