# L11n205

## Contents (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11n205 at Knotilus!

### Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $-\frac{\left(u v^2+1\right) \left(u^2+v^3\right)}{u^{3/2} v^{5/2}}$ (db) Jones polynomial $-\frac{1}{q^{7/2}}-\frac{1}{q^{17/2}}$ (db) Signature -2 (db) HOMFLY-PT polynomial $z^3 a^7+4 z a^7+2 a^7 z^{-1} -z^5 a^5-6 z^3 a^5-9 z a^5-3 a^5 z^{-1} +z a^3+a^3 z^{-1}$ (db) Kauffman polynomial $a^9 z^7-7 a^9 z^5+14 a^9 z^3-7 a^9 z-a^7 z^3+4 a^7 z-2 a^7 z^{-1} -a^6 z^6+6 a^6 z^4-9 a^6 z^2+3 a^6-a^5 z^7+7 a^5 z^5-15 a^5 z^3+12 a^5 z-3 a^5 z^{-1} -a^4 z^6+6 a^4 z^4-9 a^4 z^2+3 a^4+a^3 z-a^3 z^{-1} +a^2$ (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 \
-8-7-6-5-4-3-2-10χ
-2       110
-4       110
-6     12  1
-8      1  1
-10   121   0
-12         0
-14  11     0
-161        1
-181        1
Integral Khovanov Homology $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=-4$ $i=-2$ $i=0$ $r=-8$ ${\mathbb Z}$ ${\mathbb Z}$ $r=-7$ $r=-6$ ${\mathbb Z}$ $r=-5$ ${\mathbb Z}$ ${\mathbb Z}_2$ ${\mathbb Z}$ $r=-4$ ${\mathbb Z}_2$ ${\mathbb Z}^{2}$ $r=-3$ ${\mathbb Z}$ ${\mathbb Z}_2$ ${\mathbb Z}$ $r=-2$ ${\mathbb Z}\oplus{\mathbb Z}_2$ ${\mathbb Z}^{2}$ $r=-1$ ${\mathbb Z}_2$ ${\mathbb Z}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=0$ ${\mathbb Z}$ ${\mathbb Z}$

### Computer Talk

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