L11a72

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L11a71.gif

L11a71

L11a73.gif

L11a73

L11a72.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a72 at Knotilus!


Link Presentations

[edit Notes on L11a72's Link Presentations]

Planar diagram presentation X6172 X12,3,13,4 X20,13,21,14 X16,7,17,8 X18,9,19,10 X8,17,9,18 X10,19,11,20 X22,15,5,16 X14,21,15,22 X2536 X4,11,1,12
Gauss code {1, -10, 2, -11}, {10, -1, 4, -6, 5, -7, 11, -2, 3, -9, 8, -4, 6, -5, 7, -3, 9, -8}
A Braid Representative {{{braid_table}}}
A Morse Link Presentation L11a72 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -7 (db)
HOMFLY-PT polynomial (db)
Kauffman polynomial Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^{18} z^4-2 a^{18} z^2+a^{18}+2 a^{17} z^5-2 a^{17} z^3+3 a^{16} z^6-2 a^{16} z^4+4 a^{15} z^7-5 a^{15} z^5+4 a^{15} z^3+4 a^{14} z^8-6 a^{14} z^6+4 a^{14} z^4+a^{14} z^2+3 a^{13} z^9-5 a^{13} z^7+6 a^{13} z^5-11 a^{13} z^3+11 a^{13} z-3 a^{13} z^{-1} +a^{12} z^{10}+4 a^{12} z^8-20 a^{12} z^6+30 a^{12} z^4-24 a^{12} z^2+7 a^{12}+6 a^{11} z^9-24 a^{11} z^7+44 a^{11} z^5-53 a^{11} z^3+30 a^{11} z-7 a^{11} z^{-1} +a^{10} z^{10}+2 a^{10} z^8-19 a^{10} z^6+31 a^{10} z^4-24 a^{10} z^2+7 a^{10}+3 a^9 z^9-14 a^9 z^7+26 a^9 z^5-29 a^9 z^3+17 a^9 z-4 a^9 z^{-1} +2 a^8 z^8-8 a^8 z^6+8 a^8 z^4-a^8 z^2+a^7 z^7-5 a^7 z^5+7 a^7 z^3-2 a^7 z} (db)

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ).   
\ r
  \  
j \
-11-10-9-8-7-6-5-4-3-2-10χ
-6           11
-8          21-1
-10         3  3
-12        42  -2
-14       73   4
-16      55    0
-18     76     1
-20    45      1
-22   47       -3
-24  14        3
-26 14         -3
-28 1          1
-301           -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.

L11a71.gif

L11a71

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L11a73