L8n4

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L8n3.gif

L8n3

L8n5.gif

L8n5

L8n4.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L8n4 at Knotilus!

L8n4 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L8n4's Link Presentations]

Planar diagram presentation X6172 X5,12,6,13 X3849 X2,14,3,13 X14,7,15,8 X9,16,10,11 X11,10,12,5 X15,1,16,4
Gauss code {1, -4, -3, 8}, {-2, -1, 5, 3, -6, 7}, {-7, 2, 4, -5, -8, 6}
A Braid Representative {{{braid_table}}}
A Morse Link Presentation L8n4 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -2 (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 \
-6-5-4-3-2-10χ
-1      22
-3     121
-5    2  2
-7   12  1
-9  11   0
-11  1    1
-1311     0
-151      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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L8n3.gif

L8n3

L8n5.gif

L8n5