L11n297

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L11n296.gif

L11n296

L11n298.gif

L11n298

L11n297.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n297 at Knotilus!


Link Presentations

[edit Notes on L11n297's Link Presentations]

Planar diagram presentation X6172 X12,4,13,3 X15,20,16,21 X14,8,15,7 X21,10,22,5 X18,11,19,12 X9,17,10,16 X22,17,11,18 X8,19,9,20 X2536 X4,14,1,13
Gauss code {1, -10, 2, -11}, {10, -1, 4, -9, -7, 5}, {6, -2, 11, -4, -3, 7, 8, -6, 9, 3, -5, -8}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L11n297 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 \
-7-6-5-4-3-2-1012χ
5         11
3        21-1
1       3  3
-1      34  1
-3     41   3
-5    24    2
-7   33     0
-9  12      1
-11 13       -2
-13 1        1
-151         -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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L11n296.gif

L11n296

L11n298.gif

L11n298