L11a510

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L11a509.gif

L11a509

L11a511.gif

L11a511

L11a510.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a510 at Knotilus!


Link Presentations

[edit Notes on L11a510's Link Presentations]

Planar diagram presentation X8192 X14,3,15,4 X22,16,13,15 X10,20,11,19 X18,10,19,9 X20,12,21,11 X12,22,7,21 X16,6,17,5 X2738 X4,13,5,14 X6,18,1,17
Gauss code {1, -9, 2, -10, 8, -11}, {9, -1, 5, -4, 6, -7}, {10, -2, 3, -8, 11, -5, 4, -6, 7, -3}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gif
BraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gif
BraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gif
A Morse Link Presentation L11a510 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 4 (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 \
-4-3-2-101234567χ
19           1-1
17          2 2
15         31 -2
13        52  3
11       64   -2
9      54    1
7     67     1
5    44      0
3   37       4
1  23        -1
-1 14         3
-3 1          -1
-51           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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L11a509.gif

L11a509

L11a511.gif

L11a511