L11n446

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_3,11,4,10 X_7,15,8,14 X_13,5,14,8 X_18,12,19,11 X_22,19,17,20 X_16,21,9,22 X_20,15,21,16 X_12,18,13,17 X₂₅₃₆ X_9,1,10,4
Gauss code	{1, -10, -2, 11}, {10, -1, -3, 4}, {9, -5, 6, -8, 7, -6}, {-11, 2, 5, -9, -4, 3, 8, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 3 + u 3 + v u 2 + v w u 2 - w u 2 + v x u 2 - x u 2 - u 2 - v w u + w u - v x u - v w x u + w x u + x u + v w x - w x$ (db)
Jones polynomial	$-q^{11/2}+q^{9/2}-3 q^{7/2}+q^{5/2}-2 q^{3/2}-2 \sqrt{q}-\frac{1}{\sqrt{q}}-\frac{2}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{2}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a z 5 - z 5 a -1 - a 3 z 3 + 5 a z 3 -6 z 3 a -1 + 2 z 3 a -3 -2 a 3 z + 8 a z -12 z a -1 + 7 z a -3 - z a -5 - a 3 z -1 + 6 a z -1 -11 a -1 z -1 + 8 a -3 z -1 -2 a -5 z -1 + a z -3 -3 a -1 z -3 + 3 a -3 z -3 - a -5 z -3$ (db)
Kauffman polynomial	$- a 2 z 8 - z 8 a -2 - z 8 a -4 - z 8 -2 a 3 z 7 -3 a z 7 -4 z 7 a -1 -4 z 7 a -3 - z 7 a -5 - a 4 z 6 + 3 a 2 z 6 + 4 z 6 a -2 + 4 z 6 a -4 + 4 z 6 + 9 a 3 z 5 + 20 a z 5 + 29 z 5 a -1 + 24 z 5 a -3 + 6 z 5 a -5 + 4 a 4 z 4 + 6 a 2 z 4 + 6 z 4 a -2 + 8 z 4 -9 a 3 z 3 -36 a z 3 -57 z 3 a -1 -42 z 3 a -3 -12 z 3 a -5 -3 a 4 z 2 -14 a 2 z 2 -24 z 2 a -2 -9 z 2 a -4 -26 z 2 + 6 a 3 z + 27 a z + 44 z a -1 + 34 z a -3 + 11 z a -5 + a 4 + 6 a 2 + 21 a -2 + 9 a -4 + 18-2 a 3 z -1 -11 a z -1 -18 a -1 z -1 -14 a -3 z -1 -5 a -5 z -1 -6 a -2 z -2 -3 a -4 z -2 -3 z -2 + a z -3 + 3 a -1 z -3 + 3 a -3 z -3 + a -5 z -3$ (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 =

0 is the signature of L11n446. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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