L11n192

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_14,9,15,10 X₄₇₅₈ X_16,6,17,5 X_18,16,19,15 X_6,18,1,17 X_19,7,20,22 X_11,20,12,21 X_21,10,22,11 X_2,14,3,13 X_12,4,13,3
Gauss code	{1, -10, 11, -3, 4, -6}, {3, -1, 2, 9, -8, -11, 10, -2, 5, -4, 6, -5, -7, 8, -9, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 2 + 3 v u 2 - u 2 + 3 v 2 u -7 v u + 3 u - v 2 + 3 v -2$ (db)
Jones polynomial	$-q^{9/2}+3 q^{7/2}-6 q^{5/2}+7 q^{3/2}-9 \sqrt{q}+\frac{8}{\sqrt{q}}-\frac{7}{q^{3/2}}+\frac{5}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$a z 5 + z 5 a -1 - a 3 z 3 + 2 a z 3 + 2 z 3 a -1 - z 3 a -3 - a 3 z + a z + 2 z a -1 - z a -3 + a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$- a z 9 - z 9 a -1 -3 a 2 z 8 -2 z 8 a -2 -5 z 8 -3 a 3 z 7 -3 a z 7 - z 7 a -1 - z 7 a -3 - a 4 z 6 + 8 a 2 z 6 + 5 z 6 a -2 + 14 z 6 + 10 a 3 z 5 + 16 a z 5 + 6 z 5 a -1 + 3 a 4 z 4 -3 a 2 z 4 -9 z 4 a -2 -3 z 4 a -4 -12 z 4 -8 a 3 z 3 -13 a z 3 -6 z 3 a -1 -2 z 3 a -3 - z 3 a -5 -2 a 4 z 2 + 4 z 2 a -2 + 2 z 2 a -4 + 4 z 2 + 2 a 3 z + 3 a z + z a -5 - a -2 + a -1 z -1 + a -3 z -1$ (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 L11n192. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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