L8a8

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L8a7.gif

L8a7

L8a9.gif

L8a9

L8a8.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L8a8 at Knotilus!

L8a8 is in the Rolfsen table of links, and the "seized Carrick bend" of practical knot-tying.


The simplest Celtic or pseudo-Celtic linear decorative knot.
Alternate decorative variant
Circular arcs only
Decorative variant with big loops at ends
Coat of arms of Bressauc, Jura, Switzerland.

Link Presentations

[edit Notes on L8a8's Link Presentations]

Planar diagram presentation X8192 X10,4,11,3 X16,10,7,9 X2738 X14,12,15,11 X12,5,13,6 X4,13,5,14 X6,16,1,15
Gauss code {1, -4, 2, -7, 6, -8}, {4, -1, 3, -2, 5, -6, 7, -5, 8, -3}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L8a8 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 \
-4-3-2-101234χ
10        11
8       2 -2
6      21 1
4     32  -1
2    32   1
0   24    2
-2  22     0
-4 13      2
-6 1       -1
-81        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).

Back to the top.

L8a7.gif

L8a7

L8a9.gif

L8a9