L11n166

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_2,9,3,10 X_10,3,11,4 X_14,5,15,6 X_11,19,12,18 X_19,7,20,22 X_15,21,16,20 X_21,17,22,16 X_17,13,18,12 X₆₇₁₈ X_4,13,5,14
Gauss code	{1, -2, 3, -11, 4, -10}, {10, -1, 2, -3, -5, 9, 11, -4, -7, 8, -9, 5, -6, 7, -8, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 - v u 4 + v 2 u 3 + v u 3 - u 3 - v u 2 - v 2 u + v u + u - v -1$ (db)
Jones polynomial	$q^{7/2}-q^{5/2}+q^{3/2}-\sqrt{q}-\frac{1}{\sqrt{q}}+\frac{1}{q^{3/2}}-\frac{2}{q^{5/2}}+\frac{2}{q^{7/2}}-\frac{2}{q^{9/2}}+\frac{1}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- a z 7 -7 a z 5 + z 5 a -1 + a 5 z 3 + a 3 z 3 -15 a z 3 + 5 z 3 a -1 + 2 a 5 z + a 3 z -12 a z + 6 z a -1 + a 5 z -1 -2 a z -1 + a -1 z -1$ (db)
Kauffman polynomial	$- a z 9 - z 9 a -1 - a 2 z 8 - z 8 a -2 -2 z 8 - a 5 z 7 + 8 a z 7 + 7 z 7 a -1 - a 6 z 6 - a 4 z 6 + 8 a 2 z 6 + 7 z 6 a -2 + 15 z 6 - a 7 z 5 + 4 a 5 z 5 -20 a z 5 -15 z 5 a -1 + 3 a 6 z 4 + 3 a 4 z 4 -18 a 2 z 4 -15 z 4 a -2 -33 z 4 + 4 a 7 z 3 -5 a 5 z 3 + 22 a z 3 + 13 z 3 a -1 - a 6 z 2 -2 a 4 z 2 + 13 a 2 z 2 + 11 z 2 a -2 + 25 z 2 -3 a 7 z + 4 a 5 z -13 a z -6 z a -1 + a 4 -3 a 2 -2 a -2 -5- a 5 z -1 + 2 a z -1 + a -1 z -1$ (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 L11n166. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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