L11a69

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L11a68.gif

L11a68

L11a70.gif

L11a70

L11a69.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a69 at Knotilus!


Link Presentations

[edit Notes on L11a69's Link Presentations]

Planar diagram presentation X6172 X12,4,13,3 X14,10,15,9 X22,20,5,19 X20,11,21,12 X10,21,11,22 X18,15,19,16 X16,7,17,8 X8,17,9,18 X2536 X4,14,1,13
Gauss code {1, -10, 2, -11}, {10, -1, 8, -9, 3, -6, 5, -2, 11, -3, 7, -8, 9, -7, 4, -5, 6, -4}
A Braid Representative {{{braid_table}}}
A Morse Link Presentation L11a69 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 \
-7-6-5-4-3-2-101234χ
8           11
6          3 -3
4         61 5
2        83  -5
0       126   6
-2      1210    -2
-4     1010     0
-6    812      4
-8   610       -4
-10  28        6
-12 16         -5
-14 2          2
-161           -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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L11a68.gif

L11a68

L11a70.gif

L11a70