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

Visit L10a60 at Knotilus!

Link Presentations

[edit Notes on L10a60's Link Presentations]

Planar diagram presentation X8192 X10,4,11,3 X20,10,7,9 X14,6,15,5 X18,13,19,14 X16,19,17,20 X12,17,13,18 X2738 X4,12,5,11 X6,16,1,15
Gauss code {1, -8, 2, -9, 4, -10}, {8, -1, 3, -2, 9, -7, 5, -4, 10, -6, 7, -5, 6, -3}
A Braid Representative
A Morse Link Presentation L10a60 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{u^2 v^4-3 u^2 v^3+4 u^2 v^2-2 u^2 v-u v^4+4 u v^3-7 u v^2+4 u v-u-2 v^3+4 v^2-3 v+1}{u v^2} (db)
Jones polynomial q^{11/2}-3 q^{9/2}+6 q^{7/2}-10 q^{5/2}+11 q^{3/2}-13 \sqrt{q}+\frac{11}{\sqrt{q}}-\frac{9}{q^{3/2}}+\frac{6}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{1}{q^{9/2}} (db)
Signature 1 (db)
HOMFLY-PT polynomial z^5 a^{-3} -a^3 z^3+3 z^3 a^{-3} -2 a^3 z+3 z a^{-3} -a^3 z^{-1} -z^7 a^{-1} +2 a z^5-5 z^5 a^{-1} +7 a z^3-10 z^3 a^{-1} +8 a z-8 z a^{-1} +3 a z^{-1} -2 a^{-1} z^{-1} (db)
Kauffman polynomial z^4 a^{-6} -z^2 a^{-6} +3 z^5 a^{-5} -3 z^3 a^{-5} +z a^{-5} +a^4 z^6+5 z^6 a^{-4} -3 a^4 z^4-5 z^4 a^{-4} +3 a^4 z^2+2 z^2 a^{-4} -a^4+3 a^3 z^7+6 z^7 a^{-3} -9 a^3 z^5-8 z^5 a^{-3} +8 a^3 z^3+7 z^3 a^{-3} -3 a^3 z-3 z a^{-3} +a^3 z^{-1} +3 a^2 z^8+4 z^8 a^{-2} -4 a^2 z^6-7 a^2 z^4-8 z^4 a^{-2} +10 a^2 z^2+6 z^2 a^{-2} -3 a^2+a z^9+z^9 a^{-1} +8 a z^7+11 z^7 a^{-1} -29 a z^5-31 z^5 a^{-1} +28 a z^3+30 z^3 a^{-1} -13 a z-14 z a^{-1} +3 a z^{-1} +2 a^{-1} z^{-1} +7 z^8-10 z^6-6 z^4+10 z^2-3 (db)

Khovanov Homology

The coefficients of the monomials t^rq^j are shown, along with their alternating sums \chi (fixed j, alternation over r).   
\ r
j \
12          1-1
10         2 2
8        41 -3
6       62  4
4      65   -1
2     75    2
0    57     2
-2   46      -2
-4  25       3
-6 14        -3
-8 2         2
-101          -1
Integral Khovanov Homology

(db, data source)

\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=0 i=2
r=-5 {\mathbb Z}
r=-4 {\mathbb Z}^{2}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-3 {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=-2 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=-1 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=0 {\mathbb Z}^{7}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{7}
r=1 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r=2 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{6}
r=3 {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=4 {\mathbb Z}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=5 {\mathbb Z}_2 {\mathbb Z}

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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See/edit the Link Page master template (intermediate).

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