L11n425

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L11n424.gif

L11n424

L11n426.gif

L11n426

L11n425.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

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Link Presentations

[edit Notes on L11n425's Link Presentations]

Planar diagram presentation X8192 X16,8,17,7 X5,14,6,15 X3,10,4,11 X13,4,14,5 X17,2,18,3 X9,19,10,18 X21,7,22,12 X11,13,12,22 X20,16,21,15 X6,19,1,20
Gauss code {1, 6, -4, 5, -3, -11}, {2, -1, -7, 4, -9, 8}, {-5, 3, 10, -2, -6, 7, 11, -10, -8, 9}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart1.gif
BraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart2.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif
A Morse Link Presentation L11n425 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 \
-6-5-4-3-2-1012χ
5        22
3       21-1
1      31 2
-1     44  0
-3    21   1
-5   24    2
-7  22     0
-9  2      2
-1112       -1
-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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L11n424.gif

L11n424

L11n426.gif

L11n426