L11n160

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_16,7,17,8 X_10,4,11,3 X_2,15,3,16 X_14,10,15,9 X_11,19,12,18 X_5,13,6,12 X_6,21,1,22 X_20,14,21,13 X_22,17,7,18 X_19,4,20,5
Gauss code	{1, -4, 3, 11, -7, -8}, {2, -1, 5, -3, -6, 7, 9, -5, 4, -2, 10, 6, -11, -9, 8, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 2 + 3 v u 2 - u 2 + 3 v 2 u -7 v u + 3 u - v 2 + 3 v -2$ (db)
Jones polynomial	$q^{9/2}-3 q^{7/2}+5 q^{5/2}-7 q^{3/2}+8 \sqrt{q}-\frac{9}{\sqrt{q}}+\frac{7}{q^{3/2}}-\frac{6}{q^{5/2}}+\frac{3}{q^{7/2}}-\frac{1}{q^{9/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- a z 5 - z 5 a -1 + a 3 z 3 -2 a z 3 -2 z 3 a -1 + z 3 a -3 + a 3 z -2 a z - z a -1 + z a -3 + a 3 z -1 - a z -1$ (db)
Kauffman polynomial	$-2 a z 9 -2 z 9 a -1 -3 a 2 z 8 -4 z 8 a -2 -7 z 8 - a 3 z 7 + 5 a z 7 + 3 z 7 a -1 -3 z 7 a -3 + 11 a 2 z 6 + 14 z 6 a -2 - z 6 a -4 + 26 z 6 -3 a z 5 + 7 z 5 a -1 + 10 z 5 a -3 -3 a 4 z 4 -18 a 2 z 4 -12 z 4 a -2 + 3 z 4 a -4 -30 z 4 - a 5 z 3 - a 3 z 3 -3 a z 3 -10 z 3 a -1 -7 z 3 a -3 + 3 a 4 z 2 + 8 a 2 z 2 + 4 z 2 a -2 - z 2 a -4 + 10 z 2 + a 5 z + 3 z a -1 + 2 z a -3 - a 2 + a 3 z -1 + a z -1$ (db)

The coefficients of the monomials

t r q j

are shown, along with their alternating sums

χ

(fixed

j

, alternation over

r

). The squares with yellow highlighting are those on the "critical diagonals", where

j -2 r = s + 1

j -2 r = s -1

, where

s =

-1 is the signature of L11n160. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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