L11a482

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_2,9,3,10 X_12,3,13,4 X_10,5,11,6 X_16,11,5,12 X_4,15,1,16 X_20,14,21,13 X_18,7,19,8 X_8,17,9,18 X_22,20,17,19 X_14,22,15,21
Gauss code	{1, -2, 3, -6}, {9, -8, 10, -7, 11, -10}, {4, -1, 8, -9, 2, -4, 5, -3, 7, -11, 6, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 -2 v w u 3 + 2 w u 3 -2 u 3 -7 v u 2 + 7 v w u 2 -7 w u 2 + 7 u 2 + 7 v u -7 v w u + 7 w u -7 u -2 v + 2 v w -2 w + 2$ (db)
Jones polynomial	$- q 2 + 5 q -11 + 17 q -1 -20 q -2 + 25 q -3 -22 q -4 + 19 q -5 -13 q -6 + 7 q -7 -3 q -8 + q -9$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$z 2 a 8 + a 8 -2 z 4 a 6 -3 z 2 a 6 + a 6 z -2 -2 a 6 + z 6 a 4 + z 4 a 4 + z 2 a 4 -2 a 4 z -2 - a 4 + z 6 a 2 + z 4 a 2 + z 2 a 2 + a 2 z -2 + 2 a 2 - z 4$ (db)
Kauffman polynomial	$z 6 a 10 -3 z 4 a 10 + 3 z 2 a 10 - a 10 + 3 z 7 a 9 -8 z 5 a 9 + 7 z 3 a 9 -2 z a 9 + 4 z 8 a 8 -5 z 6 a 8 -4 z 4 a 8 + 6 z 2 a 8 - a 8 + 4 z 9 a 7 - z 7 a 7 -11 z 5 a 7 + 13 z 3 a 7 -6 z a 7 + 2 z 10 a 6 + 8 z 8 a 6 -20 z 6 a 6 + 11 z 4 a 6 + z 2 a 6 + a 6 z -2 - a 6 + 12 z 9 a 5 -17 z 7 a 5 + z 5 a 5 + 8 z 3 a 5 -2 z a 5 -2 a 5 z -1 + 2 z 10 a 4 + 17 z 8 a 4 -39 z 6 a 4 + 23 z 4 a 4 - z 2 a 4 + 2 a 4 z -2 -2 a 4 + 8 z 9 a 3 -2 z 7 a 3 -12 z 5 a 3 + 4 z 3 a 3 + 2 z a 3 -2 a 3 z -1 + 13 z 8 a 2 -20 z 6 a 2 + 7 z 4 a 2 + z 2 a 2 + a 2 z -2 -2 a 2 + 11 z 7 a -15 z 5 a + 2 z 3 a + 5 z 6 -4 z 4 + z 5 a -1$ (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 =

-2 is the signature of L11a482. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -3$	$i = -1$
$r = -8$	${\mathbb Z}$
$r = -7$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -5$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -4$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{10}$
$r = -3$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -2$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = -1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 0$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{10}$
$r = 1$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 2$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 3$	${\mathbb Z}_2$	${\mathbb Z}$