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

Visit L11a105 at Knotilus!

Link Presentations

[edit Notes on L11a105's Link Presentations]

Planar diagram presentation X6172 X14,3,15,4 X16,8,17,7 X18,10,19,9 X8,18,9,17 X22,20,5,19 X20,11,21,12 X10,21,11,22 X12,16,13,15 X2536 X4,13,1,14
Gauss code {1, -10, 2, -11}, {10, -1, 3, -5, 4, -8, 7, -9, 11, -2, 9, -3, 5, -4, 6, -7, 8, -6}
A Braid Representative
A Morse Link Presentation L11a105 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{t(1) t(2)^5-2 t(2)^5-4 t(1) t(2)^4+6 t(2)^4+6 t(1) t(2)^3-6 t(2)^3-6 t(1) t(2)^2+6 t(2)^2+6 t(1) t(2)-4 t(2)-2 t(1)+1}{\sqrt{t(1)} t(2)^{5/2}} (db)
Jones polynomial q^{11/2}-4 q^{9/2}+7 q^{7/2}-11 q^{5/2}+15 q^{3/2}-16 \sqrt{q}+\frac{15}{\sqrt{q}}-\frac{13}{q^{3/2}}+\frac{9}{q^{5/2}}-\frac{6}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{1}{q^{11/2}} (db)
Signature 1 (db)
HOMFLY-PT polynomial a^5 z+2 a^5 z^{-1} +z^5 a^{-3} -3 a^3 z^3+2 z^3 a^{-3} -8 a^3 z-4 a^3 z^{-1} -z^7 a^{-1} +3 a z^5-4 z^5 a^{-1} +10 a z^3-6 z^3 a^{-1} +9 a z-4 z a^{-1} +3 a z^{-1} - a^{-1} z^{-1} (db)
Kauffman polynomial -a^2 z^{10}-z^{10}-2 a^3 z^9-6 a z^9-4 z^9 a^{-1} -2 a^4 z^8-4 a^2 z^8-7 z^8 a^{-2} -9 z^8-a^5 z^7+2 a^3 z^7+9 a z^7-2 z^7 a^{-1} -8 z^7 a^{-3} +7 a^4 z^6+18 a^2 z^6+5 z^6 a^{-2} -7 z^6 a^{-4} +23 z^6+5 a^5 z^5+13 a^3 z^5+13 a z^5+16 z^5 a^{-1} +7 z^5 a^{-3} -4 z^5 a^{-5} -6 a^4 z^4-12 a^2 z^4+7 z^4 a^{-2} +7 z^4 a^{-4} -z^4 a^{-6} -7 z^4-9 a^5 z^3-25 a^3 z^3-25 a z^3-11 z^3 a^{-1} +z^3 a^{-3} +3 z^3 a^{-5} -a^4 z^2-3 a^2 z^2-7 z^2 a^{-2} -2 z^2 a^{-4} -7 z^2+7 a^5 z+16 a^3 z+13 a z+3 z a^{-1} -z a^{-3} +2 a^4+3 a^2+ a^{-2} +3-2 a^5 z^{-1} -4 a^3 z^{-1} -3 a z^{-1} - 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 \
12           1-1
10          3 3
8         41 -3
6        73  4
4       84   -4
2      87    1
0     89     1
-2    57      -2
-4   48       4
-6  25        -3
-8 15         4
-10 1          -1
-121           1
Integral Khovanov Homology

(db, data source)

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

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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