L11n345

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L11n344.gif

L11n344

L11n346.gif

L11n346

L11n345.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n345 at Knotilus!


Link Presentations

[edit Notes on L11n345's Link Presentations]

Planar diagram presentation X6172 X14,4,15,3 X11,19,12,18 X16,8,17,7 X17,21,18,20 X19,5,20,12 X8,22,9,21 X22,10,13,9 X10,14,11,13 X2536 X4,16,1,15
Gauss code {1, -10, 2, -11}, {10, -1, 4, -7, 8, -9, -3, 6}, {9, -2, 11, -4, -5, 3, -6, 5, 7, -8}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gif
BraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart2.gif
BraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L11n345 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 6 (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 \
-2-1012345678χ
21          11
19          11
17       21  -1
15      11   0
13     231   0
11    112    2
9   12      1
7  21       1
5 13        2
3           0
11          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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L11n344.gif

L11n344

L11n346.gif

L11n346