L11n428

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L11n427.gif

L11n427

L11n429.gif

L11n429

L11n428.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n428 at Knotilus!


Link Presentations

[edit Notes on L11n428's Link Presentations]

Planar diagram presentation X8192 X9,20,10,21 X5,15,6,14 X12,14,7,13 X16,8,17,7 X22,18,13,17 X3,10,4,11 X18,11,19,12 X15,1,16,6 X19,4,20,5 X2,21,3,22
Gauss code {1, -11, -7, 10, -3, 9}, {5, -1, -2, 7, 8, -4}, {4, 3, -9, -5, 6, -8, -10, 2, 11, -6}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif
A Morse Link Presentation L11n428 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 \
-4-3-2-1012345χ
9         1-1
7          0
5      111 1
3      1   1
1    211   2
-1   131    1
-3  111     1
-5 131      1
-7  1       1
-91         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.

L11n427.gif

L11n427

L11n429.gif

L11n429