L11a400

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,6,13,5 X₈₄₉₃ X_2,14,3,13 X_14,7,15,8 X_18,12,19,11 X_20,9,21,10 X_10,19,5,20 X_4,15,1,16 X_22,18,11,17 X_16,22,17,21
Gauss code	{1, -4, 3, -9}, {2, -1, 5, -3, 7, -8}, {6, -2, 4, -5, 9, -11, 10, -6, 8, -7, 11, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 4 -2 v u 4 - v 2 w u 4 + 2 v w u 4 - w u 4 + u 4 -2 v 2 u 3 + 4 v u 3 + 2 v 2 w u 3 -4 v w u 3 + 2 w u 3 -2 u 3 + 2 v 2 u 2 -4 v u 2 -2 v 2 w u 2 + 4 v w u 2 -2 w u 2 + 2 u 2 -2 v 2 u + 4 v u + 2 v 2 w u -4 v w u + 2 w u -2 u + v 2 -2 v - v 2 w + 2 v w - w + 1$ (db)
Jones polynomial	$q 7 -4 q 6 + 8 q 5 -14 q 4 + 18 q 3 -20 q 2 + 21 q -16 + 14 q -1 -7 q -2 + 4 q -3 - q -4$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$- z 8 a -2 -5 z 6 a -2 + z 6 a -4 + 2 z 6 - a 2 z 4 -9 z 4 a -2 + 3 z 4 a -4 + 7 z 4 -2 a 2 z 2 -5 z 2 a -2 + 2 z 2 a -4 + 5 z 2 + a 2 + 4 a -2 - a -4 -4 + 2 a 2 z -2 + 4 a -2 z -2 - a -4 z -2 -5 z -2$ (db)
Kauffman polynomial	$2 z 10 a -2 + 2 z 10 + 5 a z 9 + 13 z 9 a -1 + 8 z 9 a -3 + 4 a 2 z 8 + 18 z 8 a -2 + 13 z 8 a -4 + 9 z 8 + a 3 z 7 -14 a z 7 -32 z 7 a -1 -5 z 7 a -3 + 12 z 7 a -5 -15 a 2 z 6 -67 z 6 a -2 -24 z 6 a -4 + 8 z 6 a -6 -50 z 6 -3 a 3 z 5 + 7 a z 5 + 11 z 5 a -1 -19 z 5 a -3 -16 z 5 a -5 + 4 z 5 a -7 + 18 a 2 z 4 + 68 z 4 a -2 + 18 z 4 a -4 -6 z 4 a -6 + z 4 a -8 + 61 z 4 + 2 a 3 z 3 + a z 3 + 6 z 3 a -1 + 15 z 3 a -3 + 6 z 3 a -5 -2 z 3 a -7 -7 a 2 z 2 -24 z 2 a -2 -8 z 2 a -4 -23 z 2 + 5 a z + 9 z a -1 + 5 z a -3 + z a -5 -3 a 2 -2 a -2 -4-5 a z -1 -9 a -1 z -1 -5 a -3 z -1 - a -5 z -1 + 2 a 2 z -2 + 4 a -2 z -2 + a -4 z -2 + 5 z -2$ (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 =

2 is the signature of L11a400. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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