# L11a430

## Contents (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a430 at Knotilus!

### Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $\frac{(u-1) (v-1) (w-1) (v w-v+1) (v w-w+1)}{\sqrt{u} v^{3/2} w^{3/2}}$ (db) Jones polynomial $-q^5+4 q^4-8 q^3+14 q^2-19 q+24-22 q^{-1} +21 q^{-2} -15 q^{-3} +10 q^{-4} -5 q^{-5} + q^{-6}$ (db) Signature 0 (db) HOMFLY-PT polynomial $a^4 z^4+a^4 z^2-a^4-2 a^2 z^6-z^6 a^{-2} -6 a^2 z^4-3 z^4 a^{-2} -3 a^2 z^2-2 z^2 a^{-2} +a^2 z^{-2} + a^{-2} z^{-2} +3 a^2+ a^{-2} +z^8+5 z^6+9 z^4+4 z^2-2 z^{-2} -3$ (db) Kauffman polynomial $2 a^2 z^{10}+2 z^{10}+7 a^3 z^9+13 a z^9+6 z^9 a^{-1} +9 a^4 z^8+16 a^2 z^8+8 z^8 a^{-2} +15 z^8+5 a^5 z^7-7 a^3 z^7-19 a z^7+7 z^7 a^{-3} +a^6 z^6-21 a^4 z^6-48 a^2 z^6-9 z^6 a^{-2} +4 z^6 a^{-4} -39 z^6-10 a^5 z^5-11 a^3 z^5-2 a z^5-12 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} -a^6 z^4+12 a^4 z^4+36 a^2 z^4+2 z^4 a^{-2} -6 z^4 a^{-4} +31 z^4+3 a^5 z^3+7 a^3 z^3+8 a z^3+9 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -a^4 z^2-3 a^2 z^2+z^2 a^{-2} +2 z^2 a^{-4} -3 z^2+a^5 z+3 a^3 z+3 a z+z a^{-1} -2 a^4-6 a^2-2 a^{-2} -5-2 a z^{-1} -2 a^{-1} z^{-1} +a^2 z^{-2} + a^{-2} z^{-2} +2 z^{-2}$ (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 \
-6-5-4-3-2-1012345χ
11           1-1
9          3 3
7         51 -4
5        93  6
3       105   -5
1      149    5
-1     1214     2
-3    910      -1
-5   612       6
-7  49        -5
-9 16         5
-11 4          -4
-131           1
Integral Khovanov Homology $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=-1$ $i=1$ $r=-6$ ${\mathbb Z}$ $r=-5$ ${\mathbb Z}^{4}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-4$ ${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ $r=-3$ ${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{6}$ $r=-2$ ${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{9}$ ${\mathbb Z}^{9}$ $r=-1$ ${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{12}$ ${\mathbb Z}^{12}$ $r=0$ ${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{10}$ ${\mathbb Z}^{14}$ $r=1$ ${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{10}$ ${\mathbb Z}^{10}$ $r=2$ ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{9}$ ${\mathbb Z}^{9}$ $r=3$ ${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{5}$ $r=4$ ${\mathbb Z}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ $r=5$ ${\mathbb Z}_2$ ${\mathbb Z}$

### Computer Talk

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