L11n321

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L11n320.gif

L11n320

L11n322.gif

L11n322

L11n321.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n321 at Knotilus!


Link Presentations

[edit Notes on L11n321's Link Presentations]

Planar diagram presentation X6172 X5,14,6,15 X3849 X2,16,3,15 X16,7,17,8 X9,18,10,19 X17,1,18,4 X19,13,20,22 X13,10,14,11 X21,5,22,12 X11,21,12,20
Gauss code {1, -4, -3, 7}, {-2, -1, 5, 3, -6, 9, -11, 10}, {-9, 2, 4, -5, -7, 6, -8, 11, -10, 8}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart0.gif
A Morse Link Presentation L11n321 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 0 (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 \
-6-5-4-3-2-10123χ
7         2-2
5        3 3
3       32 -1
1      63  3
-1     56   1
-3    43    1
-5   25     3
-7  24      -2
-9 13       2
-11 1        -1
-131         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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L11n320.gif

L11n320

L11n322.gif

L11n322