L11n443

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X₂₅₃₆ X_18,11,19,12 X_3,11,4,10 X_9,1,10,4 X_7,17,8,16 X_15,5,16,8 X_20,14,21,13 X_22,19,15,20 X_12,22,13,21 X_14,17,9,18
Gauss code	{1, -2, -4, 5}, {2, -1, -6, 7}, {-5, 4, 3, -10, 8, -11}, {-7, 6, 11, -3, 9, -8, 10, -9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 2 - v u 2 - v x u 2 + x u 2 - v 2 u - v 2 w u + 2 v w u + 2 v x u - w x u - x u + v 2 w - v w - v w x + w x$ (db)
Jones polynomial	$-q^{11/2}+q^{9/2}-2 q^{7/2}-q^{5/2}-q^{3/2}-3 \sqrt{q}+\frac{1}{\sqrt{q}}-\frac{3}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{2}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$a z 5 - z 5 a -1 - a 3 z 3 + 5 a z 3 -7 z 3 a -1 + 2 z 3 a -3 -2 a 3 z + 9 a z -14 z a -1 + 8 z a -3 - z a -5 - a 3 z -1 + 6 a z -1 -11 a -1 z -1 + 8 a -3 z -1 -2 a -5 z -1 + a z -3 -3 a -1 z -3 + 3 a -3 z -3 - a -5 z -3$ (db)
Kauffman polynomial	$- a 2 z 8 - z 8 a -2 - z 8 a -4 - z 8 -2 a 3 z 7 -4 a z 7 -4 z 7 a -1 -3 z 7 a -3 - z 7 a -5 - a 4 z 6 + 2 a 2 z 6 + 5 z 6 a -2 + 5 z 6 a -4 + 3 z 6 + 9 a 3 z 5 + 23 a z 5 + 29 z 5 a -1 + 21 z 5 a -3 + 6 z 5 a -5 + 4 a 4 z 4 + 8 a 2 z 4 + 3 z 4 a -2 -3 z 4 a -4 + 10 z 4 -10 a 3 z 3 -39 a z 3 -60 z 3 a -1 -42 z 3 a -3 -11 z 3 a -5 -3 a 4 z 2 -14 a 2 z 2 -24 z 2 a -2 -7 z 2 a -4 -28 z 2 + 6 a 3 z + 30 a z + 49 z a -1 + 35 z a -3 + 10 z a -5 + a 4 + 6 a 2 + 21 a -2 + 9 a -4 + 18-2 a 3 z -1 -11 a z -1 -18 a -1 z -1 -14 a -3 z -1 -5 a -5 z -1 -6 a -2 z -2 -3 a -4 z -2 -3 z -2 + a z -3 + 3 a -1 z -3 + 3 a -3 z -3 + a -5 z -3$ (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 L11n443. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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