L10n22

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L10n21.gif

L10n21

L10n23.gif

L10n23

L10n22.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L10n22 at Knotilus!


Link Presentations

[edit Notes on L10n22's Link Presentations]

Planar diagram presentation X6172 X10,4,11,3 X12,8,13,7 X9,16,10,17 X20,17,5,18 X18,13,19,14 X14,19,15,20 X15,8,16,9 X2536 X4,12,1,11
Gauss code {1, -9, 2, -10}, {9, -1, 3, 8, -4, -2, 10, -3, 6, -7, -8, 4, 5, -6, 7, -5}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gif
BraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gif
BraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L10n22 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -1 (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 \
-7-6-5-4-3-2-101χ
2        1-1
0       3 3
-2      33 0
-4     31  2
-6    23   1
-8   33    0
-10  12     1
-12 13      -2
-14 1       1
-161        -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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L10n21.gif

L10n21

L10n23.gif

L10n23