# L11a60

## Contents (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a60 at Knotilus!

### Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $-\frac{2 t(1) t(2)^3-4 t(2)^3-8 t(1) t(2)^2+11 t(2)^2+11 t(1) t(2)-8 t(2)-4 t(1)+2}{\sqrt{t(1)} t(2)^{3/2}}$ (db) Jones polynomial $q^{9/2}-\frac{6}{q^{9/2}}-4 q^{7/2}+\frac{9}{q^{7/2}}+7 q^{5/2}-\frac{13}{q^{5/2}}-11 q^{3/2}+\frac{16}{q^{3/2}}-\frac{1}{q^{13/2}}+\frac{2}{q^{11/2}}+14 \sqrt{q}-\frac{16}{\sqrt{q}}$ (db) Signature -1 (db) HOMFLY-PT polynomial $a^7 z^{-1} -3 a^5 z-a^5 z^{-1} +3 a^3 z^3+z^3 a^{-3} +a^3 z-a^3 z^{-1} -a z^5-z^5 a^{-1} +a z^3-z^3 a^{-1} +2 a z+2 a z^{-1} -2 z a^{-1} - a^{-1} z^{-1}$ (db) Kauffman polynomial $-a^2 z^{10}-z^{10}-2 a^3 z^9-6 a z^9-4 z^9 a^{-1} -3 a^4 z^8-5 a^2 z^8-6 z^8 a^{-2} -8 z^8-3 a^5 z^7-4 a^3 z^7+8 a z^7+5 z^7 a^{-1} -4 z^7 a^{-3} -2 a^6 z^6+a^4 z^6+10 a^2 z^6+17 z^6 a^{-2} -z^6 a^{-4} +25 z^6-a^7 z^5+3 a^5 z^5+12 a^3 z^5+5 a z^5+8 z^5 a^{-1} +11 z^5 a^{-3} +3 a^6 z^4+a^4 z^4-9 a^2 z^4-12 z^4 a^{-2} +2 z^4 a^{-4} -21 z^4+3 a^7 z^3+a^5 z^3-14 a^3 z^3-18 a z^3-12 z^3 a^{-1} -6 z^3 a^{-3} +2 a^4 z^2+6 a^2 z^2+2 z^2 a^{-2} +6 z^2-3 a^7 z-2 a^5 z+8 a^3 z+12 a z+5 z a^{-1} -a^6-2 a^4-3 a^2-1+a^7 z^{-1} +a^5 z^{-1} -a^3 z^{-1} -2 a z^{-1} - a^{-1} z^{-1}$ (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 \
-6-5-4-3-2-1012345χ
10           1-1
8          3 3
6         41 -3
4        73  4
2       74   -3
0      97    2
-2     88     0
-4    58      -3
-6   48       4
-8  25        -3
-10 15         4
-12 1          -1
-141           1
Integral Khovanov Homology $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=-2$ $i=0$ $r=-6$ ${\mathbb Z}$ $r=-5$ ${\mathbb Z}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-4$ ${\mathbb Z}^{5}\oplus{\mathbb Z}_2$ ${\mathbb Z}^{2}$ $r=-3$ ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ $r=-2$ ${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{5}$ $r=-1$ ${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{8}$ ${\mathbb Z}^{8}$ $r=0$ ${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{8}$ ${\mathbb Z}^{9}$ $r=1$ ${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ $r=2$ ${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ $r=3$ ${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ $r=4$ ${\mathbb Z}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ $r=5$ ${\mathbb Z}_2$ ${\mathbb Z}$

### Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory. See A Sample KnotTheory Session.