L9a31

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L9a30.gif

L9a30

L9a32.gif

L9a32

L9a31.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9a31 at Knotilus!

L9a31 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L9a31's Link Presentations]

Planar diagram presentation X8192 X16,9,17,10 X6718 X18,13,7,14 X10,4,11,3 X14,6,15,5 X4,12,5,11 X12,17,13,18 X2,16,3,15
Gauss code {1, -9, 5, -7, 6, -3}, {3, -1, 2, -5, 7, -8, 4, -6, 9, -2, 8, -4}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gif
BraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif
A Morse Link Presentation L9a31 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 \
-5-4-3-2-101234χ
8         11
6        2 -2
4       41 3
2      43  -1
0     63   3
-2    45    1
-4   45     -1
-6  24      2
-8 14       -3
-10 2        2
-121         -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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L9a30.gif

L9a30

L9a32.gif

L9a32