L11n190

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_12,3,13,4 X_22,10,7,9 X_10,14,11,13 X_5,16,6,17 X_20,15,21,16 X_18,21,19,22 X_14,19,15,20 X₂₇₃₈ X_4,11,5,12 X_17,6,18,1
Gauss code	{1, -9, 2, -10, -5, 11}, {9, -1, 3, -4, 10, -2, 4, -8, 6, 5, -11, -7, 8, -6, 7, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$u 4 - v 2 u 3 + 4 v u 3 -3 u 3 + 4 v 2 u 2 -7 v u 2 + 4 u 2 -3 v 2 u + 4 v u - u + v 2$ (db)
Jones polynomial	$-\frac{2}{q^{3/2}}+\frac{5}{q^{5/2}}-\frac{8}{q^{7/2}}+\frac{10}{q^{9/2}}-\frac{12}{q^{11/2}}+\frac{10}{q^{13/2}}-\frac{9}{q^{15/2}}+\frac{6}{q^{17/2}}-\frac{3}{q^{19/2}}+\frac{1}{q^{21/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 11 z -1 + 4 z a 9 + 3 a 9 z -1 -4 z 3 a 7 -6 z a 7 -2 a 7 z -1 + z 5 a 5 + z 3 a 5 + z a 5 -2 z 3 a 3 -2 z a 3$ (db)
Kauffman polynomial	$- z 6 a 12 + 3 z 4 a 12 -3 z 2 a 12 + a 12 -3 z 7 a 11 + 9 z 5 a 11 -8 z 3 a 11 + 3 z a 11 - a 11 z -1 -3 z 8 a 10 + 4 z 6 a 10 + 8 z 4 a 10 -11 z 2 a 10 + 3 a 10 - z 9 a 9 -7 z 7 a 9 + 26 z 5 a 9 -24 z 3 a 9 + 12 z a 9 -3 a 9 z -1 -6 z 8 a 8 + 8 z 6 a 8 + 7 z 4 a 8 -9 z 2 a 8 + 3 a 8 - z 9 a 7 -7 z 7 a 7 + 19 z 5 a 7 -16 z 3 a 7 + 7 z a 7 -2 a 7 z -1 -3 z 8 a 6 + 2 z 6 a 6 -2 z 4 a 6 + 2 z 2 a 6 -3 z 7 a 5 + 2 z 5 a 5 -3 z 3 a 5 - z 6 a 4 -4 z 4 a 4 + 3 z 2 a 4 -3 z 3 a 3 + 2 z a 3$ (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 =

-3 is the signature of L11n190. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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