L11n42

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L11n41.gif

L11n41

L11n43.gif

L11n43

L11n42.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n42 at Knotilus!


Link Presentations

[edit Notes on L11n42's Link Presentations]

Planar diagram presentation X6172 X12,7,13,8 X4,13,1,14 X9,18,10,19 X3849 X5,14,6,15 X15,22,16,5 X17,20,18,21 X21,16,22,17 X19,10,20,11 X11,2,12,3
Gauss code {1, 11, -5, -3}, {-6, -1, 2, 5, -4, 10, -11, -2, 3, 6, -7, 9, -8, 4, -10, 8, -9, 7}
A Braid Representative
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A Morse Link Presentation L11n42 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -5 (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 \
-9-8-7-6-5-4-3-2-10χ
-4         11
-6        110
-8       2  2
-10      21  -1
-12     42   2
-14    33    0
-16   33     0
-18  13      2
-20 23       -1
-22 1        1
-242         -2
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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L11n41

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L11n43