L10n12

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L10n11.gif

L10n11

L10n13.gif

L10n13

L10n12.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L10n12 at Knotilus!


Link Presentations

[edit Notes on L10n12's Link Presentations]

Planar diagram presentation X6172 X14,7,15,8 X4,15,1,16 X5,12,6,13 X8493 X9,16,10,17 X17,20,18,5 X11,19,12,18 X19,11,20,10 X2,14,3,13
Gauss code {1, -10, 5, -3}, {-4, -1, 2, -5, -6, 9, -8, 4, 10, -2, 3, 6, -7, 8, -9, 7}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart4.gif
A Morse Link Presentation L10n12 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 \
-6-5-4-3-2-1012χ
4        22
2       1 -1
0      52 3
-2     43  -1
-4    33   0
-6   34    1
-8  23     -1
-10 13      2
-12 2       -2
-141        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).

Back to the top.

L10n11.gif

L10n11

L10n13.gif

L10n13