L9n20

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L9n19.gif

L9n19

L9n21.gif

L9n21

L9n20.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9n20 at Knotilus!

L9n20 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L9n20's Link Presentations]

Planar diagram presentation X6172 X3,11,4,10 X7,15,8,14 X13,5,14,8 X11,17,12,16 X15,9,16,18 X17,13,18,12 X2536 X9,1,10,4
Gauss code {1, -8, -2, 9}, {8, -1, -3, 4}, {-9, 2, -5, 7, -4, 3, -6, 5, -7, 6}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart1.gifBraidPart2.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart1.gifBraidPart2.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L9n20 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 2 (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 z^7 a^{-5} +z^7 a^{-7} +4 z^6 a^{-4} +6 z^6 a^{-6} +2 z^6 a^{-8} +3 z^5 a^{-3} +5 z^5 a^{-5} +3 z^5 a^{-7} +z^5 a^{-9} -11 z^4 a^{-4} -16 z^4 a^{-6} -5 z^4 a^{-8} -6 z^3 a^{-3} -18 z^3 a^{-5} -15 z^3 a^{-7} -3 z^3 a^{-9} +6 z^2 a^{-2} +18 z^2 a^{-4} +15 z^2 a^{-6} +3 z^2 a^{-8} +11 z a^{-3} +21 z a^{-5} +13 z a^{-7} +3 z a^{-9} -7 a^{-2} -14 a^{-4} -10 a^{-6} -2 a^{-8} -5 a^{-3} z^{-1} -9 a^{-5} z^{-1} -5 a^{-7} z^{-1} - a^{-9} z^{-1} +2 a^{-2} z^{-2} +5 a^{-4} z^{-2} +4 a^{-6} z^{-2} + a^{-8} z^{-2} } (db)

Khovanov Homology

The coefficients of the monomials 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 t^rq^j} are shown, along with their alternating sums 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 \chi} (fixed 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 j} , alternation over ).   
\ r
  \  
j \
01234567χ
17       1-1
15      1 1
13     31 -2
11    21  1
9   34   1
7  31    2
5  3     3
333      0
13       3
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

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L9n19.gif

L9n19

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L9n21