L11n426

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_16,8,17,7 X_14,6,15,5 X_3,10,4,11 X_4,14,5,13 X_17,2,18,3 X_9,19,10,18 X_12,21,7,22 X_22,11,13,12 X_20,16,21,15 X_6,19,1,20
Gauss code	{1, 6, -4, -5, 3, -11}, {2, -1, -7, 4, 9, -8}, {5, -3, 10, -2, -6, 7, 11, -10, 8, -9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- w u 2 + u 2 -2 v u + 2 v w u + v 2 - v 2 w$ (db)
Jones polynomial	$- q 3 + q 2 + 2 + q -1 + q -3 - q -4 + q -5$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z 2 a 4 + a 4 z -2 + 2 a 4 - z 4 a 2 -5 z 2 a 2 -2 a 2 z -2 -7 a 2 + z 4 + 5 z 2 + z -2 + 7- z 2 a -2 -2 a -2$ (db)
Kauffman polynomial	$a 3 z 9 + a z 9 + a 4 z 8 + 2 a 2 z 8 + z 8 -7 a 3 z 7 -7 a z 7 -7 a 4 z 6 -15 a 2 z 6 -8 z 6 + 14 a 3 z 5 + 13 a z 5 - z 5 a -1 + 15 a 4 z 4 + 35 a 2 z 4 + z 4 a -2 + 21 z 4 -7 a 3 z 3 -3 a z 3 + 5 z 3 a -1 + z 3 a -3 -12 a 4 z 2 -32 a 2 z 2 -4 z 2 a -2 -24 z 2 -3 a 3 z -7 a z -6 z a -1 -2 z a -3 + 5 a 4 + 13 a 2 + 4 a -2 + 13 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 L11n426. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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