L10n21

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L10n20.gif

L10n20

L10n22.gif

L10n22

L10n21.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L10n21 at Knotilus!


Link Presentations

[edit Notes on L10n21's Link Presentations]

Planar diagram presentation X6172 X10,4,11,3 X12,8,13,7 X9,16,10,17 X17,5,18,20 X13,19,14,18 X19,15,20,14 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.gifBraidPart1.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart2.gif
BraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L10n21 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 \
-2-10123456χ
14        11
12       2 -2
10      21 1
8     32  -1
6    32   1
4   23    1
2  33     0
0 14      3
-2 1       -1
-41        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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L10n20.gif

L10n20

L10n22.gif

L10n22