L11n288

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L11n287.gif

L11n287

L11n289.gif

L11n289

L11n288.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

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Link Presentations

[edit Notes on L11n288's Link Presentations]

Planar diagram presentation X6172 X5,12,6,13 X3849 X13,2,14,3 X14,7,15,8 X11,18,12,19 X9,21,10,20 X19,5,20,10 X4,15,1,16 X17,22,18,11 X21,16,22,17
Gauss code {1, 4, -3, -9}, {-2, -1, 5, 3, -7, 8}, {-6, 2, -4, -5, 9, 11, -10, 6, -8, 7, -11, 10}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif
A Morse Link Presentation L11n288 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -6 (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 \
-7-6-5-4-3-2-1012χ
-1         11
-3          0
-5       31 2
-7     111  1
-9     42   2
-11   222    2
-13   32     1
-15 122      1
-17 12       -1
-1911        0
-211         -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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L11n287.gif

L11n287

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L11n289