L9a15

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L9a14.gif

L9a14

L9a16.gif

L9a16

L9a15.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9a15 at Knotilus!

L9a15 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L9a15's Link Presentations]

Planar diagram presentation X6172 X12,4,13,3 X14,8,15,7 X18,12,5,11 X8,18,9,17 X16,10,17,9 X10,16,11,15 X2536 X4,14,1,13
Gauss code {1, -8, 2, -9}, {8, -1, 3, -5, 6, -7, 4, -2, 9, -3, 7, -6, 5, -4}
A Braid Representative {{{braid_table}}}
A Morse Link Presentation L9a15 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 3 (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 \
-2-101234567χ
18         1-1
16        1 1
14       31 -2
12      31  2
10     43   -1
8    33    0
6   24     2
4  33      0
2 14       3
0 1        -1
-21         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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L9a14.gif

L9a14

L9a16.gif

L9a16