L11n196

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_12,3,13,4 X_13,21,14,20 X_16,9,17,10 X_10,19,11,20 X_15,7,16,22 X_21,15,22,14 X_18,5,19,6 X₂₇₃₈ X_4,11,5,12 X_6,17,1,18
Gauss code	{1, -9, 2, -10, 8, -11}, {9, -1, 4, -5, 10, -2, -3, 7, -6, -4, 11, -8, 5, 3, -7, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 4 + u 4 - v 2 u 3 + 4 v u 3 -4 u 3 + 3 v 2 u 2 -7 v u 2 + 3 u 2 -4 v 2 u + 4 v u - u + v 2 - v$ (db)
Jones polynomial	$q^{5/2}-4 q^{3/2}+7 \sqrt{q}-\frac{10}{\sqrt{q}}+\frac{12}{q^{3/2}}-\frac{12}{q^{5/2}}+\frac{10}{q^{7/2}}-\frac{8}{q^{9/2}}+\frac{4}{q^{11/2}}-\frac{2}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a 7 z -1 + z 3 a 5 - z a 5 - a 5 z -1 - z 5 a 3 - z 3 a 3 - z a 3 - z 5 a - z 3 a - z a + z 3 a -1$ (db)
Kauffman polynomial	$- a 5 z 9 - a 3 z 9 - a 6 z 8 -5 a 4 z 8 -4 a 2 z 8 - a 5 z 7 -8 a 3 z 7 -7 a z 7 + 5 a 4 z 6 -2 a 2 z 6 -7 z 6 -3 a 7 z 5 + 2 a 5 z 5 + 16 a 3 z 5 + 7 a z 5 -4 z 5 a -1 + 2 a 6 z 4 + 5 a 4 z 4 + 12 a 2 z 4 - z 4 a -2 + 8 z 4 + 8 a 7 z 3 + 4 a 5 z 3 -7 a 3 z 3 + 3 z 3 a -1 + a 6 z 2 -4 a 4 z 2 -7 a 2 z 2 -2 z 2 -6 a 7 z -4 a 5 z + a 3 z - a z - a 6 + a 7 z -1 + a 5 z -1$ (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 L11n196. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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