# L11a244

## Contents (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a244 at Knotilus!

### Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $\frac{t(1)^2 t(2)^4-2 t(1) t(2)^4-5 t(1)^2 t(2)^3+11 t(1) t(2)^3-6 t(2)^3+9 t(1)^2 t(2)^2-19 t(1) t(2)^2+9 t(2)^2-6 t(1)^2 t(2)+11 t(1) t(2)-5 t(2)-2 t(1)+1}{t(1) t(2)^2}$ (db) Jones polynomial $q^{9/2}-\frac{11}{q^{9/2}}-5 q^{7/2}+\frac{17}{q^{7/2}}+11 q^{5/2}-\frac{25}{q^{5/2}}-18 q^{3/2}+\frac{28}{q^{3/2}}-\frac{1}{q^{13/2}}+\frac{4}{q^{11/2}}+25 \sqrt{q}-\frac{28}{\sqrt{q}}$ (db) Signature -1 (db) HOMFLY-PT polynomial $a^5 z^3+a^5 z+2 a^5 z^{-1} -2 a^3 z^5-4 a^3 z^3+z^3 a^{-3} -6 a^3 z-3 a^3 z^{-1} +a z^7+3 a z^5-2 z^5 a^{-1} +6 a z^3-3 z^3 a^{-1} +4 a z-2 z a^{-1} +a z^{-1}$ (db) Kauffman polynomial $-3 a^2 z^{10}-3 z^{10}-10 a^3 z^9-19 a z^9-9 z^9 a^{-1} -13 a^4 z^8-24 a^2 z^8-10 z^8 a^{-2} -21 z^8-10 a^5 z^7+3 a^3 z^7+26 a z^7+8 z^7 a^{-1} -5 z^7 a^{-3} -4 a^6 z^6+18 a^4 z^6+62 a^2 z^6+21 z^6 a^{-2} -z^6 a^{-4} +62 z^6-a^7 z^5+16 a^5 z^5+17 a^3 z^5+5 a z^5+14 z^5 a^{-1} +9 z^5 a^{-3} +3 a^6 z^4-8 a^4 z^4-46 a^2 z^4-13 z^4 a^{-2} +z^4 a^{-4} -49 z^4+a^7 z^3-15 a^5 z^3-16 a^3 z^3-9 a z^3-13 z^3 a^{-1} -4 z^3 a^{-3} -3 a^4 z^2+9 a^2 z^2+2 z^2 a^{-2} +14 z^2+8 a^5 z+7 a^3 z+z a^{-1} +3 a^4+3 a^2+1-2 a^5 z^{-1} -3 a^3 z^{-1} -a z^{-1}$ (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          4 4
6         71 -6
4        114  7
2       147   -7
0      1411    3
-2     1515     0
-4    1013      -3
-6   715       8
-8  410        -6
-10  7         7
-1214          -3
-141           1
Integral Khovanov Homology $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=-2$ $i=0$ $r=-6$ ${\mathbb Z}$ ${\mathbb Z}$ $r=-5$ ${\mathbb Z}^{4}$ $r=-4$ ${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ $r=-3$ ${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ $r=-2$ ${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{10}$ ${\mathbb Z}^{10}$ $r=-1$ ${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{15}$ ${\mathbb Z}^{15}$ $r=0$ ${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{13}$ ${\mathbb Z}^{14}$ $r=1$ ${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{14}$ ${\mathbb Z}^{14}$ $r=2$ ${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{11}$ ${\mathbb Z}^{11}$ $r=3$ ${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ $r=4$ ${\mathbb Z}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ $r=5$ ${\mathbb Z}_2$ ${\mathbb Z}$

### Computer Talk

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