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

Visit L11a100 at Knotilus!

Link Presentations

[edit Notes on L11a100's Link Presentations]

Planar diagram presentation X6172 X16,7,17,8 X18,9,19,10 X20,11,21,12 X8,17,9,18 X10,19,11,20 X4,21,1,22 X14,6,15,5 X12,4,13,3 X22,14,5,13 X2,16,3,15
Gauss code {1, -11, 9, -7}, {8, -1, 2, -5, 3, -6, 4, -9, 10, -8, 11, -2, 5, -3, 6, -4, 7, -10}
A Braid Representative
A Morse Link Presentation L11a100 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{(u-1) (v-1) \left(v^2-v+1\right)^2 \left(v^2+v+1\right)}{\sqrt{u} v^{7/2}} (db)
Jones polynomial -q^{5/2}+3 q^{3/2}-5 \sqrt{q}+\frac{6}{\sqrt{q}}-\frac{10}{q^{3/2}}+\frac{10}{q^{5/2}}-\frac{11}{q^{7/2}}+\frac{10}{q^{9/2}}-\frac{7}{q^{11/2}}+\frac{5}{q^{13/2}}-\frac{3}{q^{15/2}}+\frac{1}{q^{17/2}} (db)
Signature -3 (db)
HOMFLY-PT polynomial a^3 z^9-a^5 z^7+7 a^3 z^7-a z^7-5 a^5 z^5+17 a^3 z^5-5 a z^5-7 a^5 z^3+17 a^3 z^3-7 a z^3-3 a^5 z+7 a^3 z-4 a z-a^5 z^{-1} +3 a^3 z^{-1} -2 a z^{-1} (db)
Kauffman polynomial a^{10} z^4-a^{10} z^2+3 a^9 z^5-4 a^9 z^3+4 a^8 z^6-5 a^8 z^4+a^8 z^2+4 a^7 z^7-5 a^7 z^5+2 a^7 z^3+4 a^6 z^8-8 a^6 z^6+7 a^6 z^4-2 a^6 z^2+a^6+4 a^5 z^9-14 a^5 z^7+23 a^5 z^5-18 a^5 z^3+6 a^5 z-a^5 z^{-1} +2 a^4 z^{10}-4 a^4 z^8-3 a^4 z^6+11 a^4 z^4-8 a^4 z^2+3 a^4+8 a^3 z^9-38 a^3 z^7+63 a^3 z^5-46 a^3 z^3+13 a^3 z-3 a^3 z^{-1} +2 a^2 z^{10}-5 a^2 z^8-4 a^2 z^6+11 a^2 z^4-6 a^2 z^2+3 a^2+4 a z^9-19 a z^7+z^7 a^{-1} +28 a z^5-4 z^5 a^{-1} -19 a z^3+3 z^3 a^{-1} +7 a z-2 a z^{-1} +3 z^8-13 z^6+13 z^4-2 z^2 (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 \
6           11
4          2 -2
2         31 2
0        32  -1
-2       73   4
-4      55    0
-6     65     1
-8    45      1
-10   36       -3
-12  24        2
-14 13         -2
-16 2          2
-181           -1
Integral Khovanov Homology

(db, data source)

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