L11n421

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L11n420.gif

L11n420

L11n422.gif

L11n422

L11n421.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n421 at Knotilus!


Link Presentations

[edit Notes on L11n421's Link Presentations]

Planar diagram presentation X8192 X16,8,17,7 X3,10,4,11 X17,2,18,3 X9,19,10,18 X20,12,21,11 X14,6,15,5 X22,15,13,16 X6,14,1,13 X4,19,5,20 X12,22,7,21
Gauss code {1, 4, -3, -10, 7, -9}, {2, -1, -5, 3, 6, -11}, {9, -7, 8, -2, -4, 5, 10, -6, 11, -8}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif
A Morse Link Presentation L11n421 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 2 (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 \
-5-4-3-2-101234χ
11         11
9        110
7       2  2
5      22  0
3     21   1
1    23    1
-1   21     1
-3  13      2
-5 11       0
-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.

L11n420.gif

L11n420

L11n422.gif

L11n422