L11n169

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L11n168.gif

L11n168

L11n170.gif

L11n170

L11n169.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

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Link Presentations

[edit Notes on L11n169's Link Presentations]

Planar diagram presentation X8192 X2,9,3,10 X10,3,11,4 X14,5,15,6 X15,20,16,21 X11,18,12,19 X19,12,20,13 X17,22,18,7 X21,16,22,17 X6718 X4,13,5,14
Gauss code {1, -2, 3, -11, 4, -10}, {10, -1, 2, -3, -6, 7, 11, -4, -5, 9, -8, 6, -7, 5, -9, 8}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gif
BraidPart4.gifBraidPart3.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart4.gif
BraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart0.gif
A Morse Link Presentation L11n169 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -7 (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 \
-11-10-9-8-7-6-5-4-3-2-10χ
-8           11
-10           11
-12         1  1
-14       2    2
-16      111   -1
-18     32     1
-20    221     -1
-22   22       0
-24  12        1
-26 12         -1
-28 1          1
-301           -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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L11n168.gif

L11n168

L11n170.gif

L11n170