L11a168

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L11a167.gif

L11a167

L11a169.gif

L11a169

L11a168.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a168 at Knotilus!


Link Presentations

[edit Notes on L11a168's Link Presentations]

Planar diagram presentation X8192 X18,11,19,12 X10,4,11,3 X2,17,3,18 X14,5,15,6 X6718 X16,10,17,9 X20,13,21,14 X12,19,13,20 X22,16,7,15 X4,22,5,21
Gauss code {1, -4, 3, -11, 5, -6}, {6, -1, 7, -3, 2, -9, 8, -5, 10, -7, 4, -2, 9, -8, 11, -10}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart3.gif
BraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart4.gif
A Morse Link Presentation L11a168 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 \
-7-6-5-4-3-2-101234χ
6           11
4          3 -3
2         51 4
0        73  -4
-2       115   6
-4      98    -1
-6     1110     1
-8    810      2
-10   510       -5
-12  38        5
-14 15         -4
-16 3          3
-181           -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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L11a167.gif

L11a167

L11a169.gif

L11a169