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

Visit L11a102 at Knotilus!

Link Presentations

[edit Notes on L11a102's Link Presentations]

Planar diagram presentation X6172 X18,7,19,8 X20,9,21,10 X8,19,9,20 X4,21,1,22 X14,6,15,5 X12,4,13,3 X22,14,5,13 X16,11,17,12 X2,16,3,15 X10,17,11,18
Gauss code {1, -10, 7, -5}, {6, -1, 2, -4, 3, -11, 9, -7, 8, -6, 10, -9, 11, -2, 4, -3, 5, -8}
A Braid Representative
A Morse Link Presentation L11a102 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{(t(1)-1) (t(2)-1) \left(t(2)^2-t(2)+1\right) \left(2 t(2)^2-t(2)+2\right)}{\sqrt{t(1)} t(2)^{5/2}} (db)
Jones polynomial -\frac{13}{q^{9/2}}-q^{7/2}+\frac{17}{q^{7/2}}+3 q^{5/2}-\frac{19}{q^{5/2}}-7 q^{3/2}+\frac{19}{q^{3/2}}+\frac{1}{q^{15/2}}-\frac{4}{q^{13/2}}+\frac{8}{q^{11/2}}+11 \sqrt{q}-\frac{17}{\sqrt{q}} (db)
Signature -1 (db)
HOMFLY-PT polynomial -a^5 z^5-2 a^5 z^3+a^5 z^{-1} +a^3 z^7+3 a^3 z^5+a^3 z^3-4 a^3 z-3 a^3 z^{-1} +a z^7+4 a z^5-z^5 a^{-1} +7 a z^3-3 z^3 a^{-1} +7 a z-3 z a^{-1} +4 a z^{-1} -2 a^{-1} z^{-1} (db)
Kauffman polynomial -2 a^4 z^{10}-2 a^2 z^{10}-5 a^5 z^9-10 a^3 z^9-5 a z^9-6 a^6 z^8-5 a^4 z^8-6 a^2 z^8-7 z^8-4 a^7 z^7+7 a^5 z^7+21 a^3 z^7+4 a z^7-6 z^7 a^{-1} -a^8 z^6+13 a^6 z^6+13 a^4 z^6+17 a^2 z^6-3 z^6 a^{-2} +15 z^6+10 a^7 z^5-a^5 z^5-17 a^3 z^5+9 a z^5+14 z^5 a^{-1} -z^5 a^{-3} +2 a^8 z^4-5 a^6 z^4-12 a^2 z^4+5 z^4 a^{-2} -14 z^4-6 a^7 z^3+6 a^5 z^3+3 a^3 z^3-25 a z^3-14 z^3 a^{-1} +2 z^3 a^{-3} -a^8 z^2-a^6 z^2-5 a^4 z^2-4 a^2 z^2+z^2-a^7 z-2 a^5 z+7 a^3 z+15 a z+7 z a^{-1} +a^6+3 a^4+3 a^2+2-a^5 z^{-1} -3 a^3 z^{-1} -4 a z^{-1} -2 a^{-1} z^{-1} (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 \
8           11
6          2 -2
4         51 4
2        62  -4
0       115   6
-2      108    -2
-4     99     0
-6    810      2
-8   59       -4
-10  38        5
-12 15         -4
-14 3          3
-161           -1
Integral Khovanov Homology

(db, data source)

\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-2 i=0
r=-7 {\mathbb Z}
r=-6 {\mathbb Z}^{3}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-5 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r=-4 {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-3 {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{8} {\mathbb Z}^{8}
r=-2 {\mathbb Z}^{10}\oplus{\mathbb Z}_2^{9} {\mathbb Z}^{9}
r=-1 {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{10} {\mathbb Z}^{10}
r=0 {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{9} {\mathbb Z}^{11}
r=1 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r=2 {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=3 {\mathbb Z}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=4 {\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

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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