L11a366

(Knotscape image)

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

Planar diagram presentation	X_12,1,13,2 X_14,3,15,4 X_16,5,17,6 X_6,11,7,12 X_18,8,19,7 X_22,18,11,17 X_20,10,21,9 X_8,20,9,19 X_10,22,1,21 X_4,13,5,14 X_2,15,3,16
Gauss code	{1, -11, 2, -10, 3, -4, 5, -8, 7, -9}, {4, -1, 10, -2, 11, -3, 6, -5, 8, -7, 9, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 3 u 4 + v 2 u 4 - v 4 u 3 + 3 v 3 u 3 -4 v 2 u 3 + 2 v u 3 + v 4 u 2 -4 v 3 u 2 + 5 v 2 u 2 -4 v u 2 + u 2 + 2 v 3 u -4 v 2 u + 3 v u - u + v 2 - v$ (db)
Jones polynomial	$q^{11/2}-3 q^{9/2}+6 q^{7/2}-9 q^{5/2}+11 q^{3/2}-13 \sqrt{q}+\frac{11}{\sqrt{q}}-\frac{10}{q^{3/2}}+\frac{7}{q^{5/2}}-\frac{4}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{1}{q^{11/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- a z 7 - z 7 a -1 + a 3 z 5 -5 a z 5 -4 z 5 a -1 + z 5 a -3 + 4 a 3 z 3 -9 a z 3 -4 z 3 a -1 + 3 z 3 a -3 + 4 a 3 z -7 a z + 2 z a -3 + a 3 z -1 - a z -1$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 -2 a 3 z 9 -5 a z 9 -3 z 9 a -1 -2 a 4 z 8 -5 z 8 a -2 -3 z 8 - a 5 z 7 + 7 a 3 z 7 + 17 a z 7 + 3 z 7 a -1 -6 z 7 a -3 + 9 a 4 z 6 + 8 a 2 z 6 + 8 z 6 a -2 -5 z 6 a -4 + 12 z 6 + 5 a 5 z 5 -7 a 3 z 5 -24 a z 5 + z 5 a -1 + 10 z 5 a -3 -3 z 5 a -5 -12 a 4 z 4 -10 a 2 z 4 -6 z 4 a -2 + 6 z 4 a -4 - z 4 a -6 -11 z 4 -7 a 5 z 3 + 5 a 3 z 3 + 23 a z 3 - z 3 a -1 -9 z 3 a -3 + 3 z 3 a -5 + 5 a 4 z 2 + 6 a 2 z 2 + z 2 a -2 -2 z 2 a -4 + z 2 a -6 + 5 z 2 + 2 a 5 z -4 a 3 z -10 a z - z a -1 + 3 z a -3 - a 2 + a 3 z -1 + a z -1$ (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 L11a366. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 0$	$i = 2$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -2$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{5}$
$r = -1$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 0$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{7}$
$r = 1$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 3$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$