L11n216

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_12,3,13,4 X_18,8,19,7 X_14,6,15,5 X_17,9,18,22 X_21,17,22,16 X_20,13,21,14 X_6,16,7,15 X_4,20,5,19 X_2,9,3,10 X_8,11,1,12
Gauss code	{1, -10, 2, -9, 4, -8, 3, -11}, {10, -1, 11, -2, 7, -4, 8, 6, -5, -3, 9, -7, -6, 5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 3 + v u 3 - v 3 u 2 + 4 v 2 u 2 -4 v u 2 + u 2 + v 3 u -4 v 2 u + 4 v u - u + v 2 - v$ (db)
Jones polynomial	$-q^{13/2}+3 q^{11/2}-5 q^{9/2}+7 q^{7/2}-8 q^{5/2}+8 q^{3/2}-8 \sqrt{q}+\frac{4}{\sqrt{q}}-\frac{3}{q^{3/2}}+\frac{1}{q^{5/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z 5 a -1 + z 5 a -3 - a z 3 + 2 z 3 a -1 + 2 z 3 a -3 - z 3 a -5 - a z + z a -1 + z a -3 - z a -5 + a z -1 - a -1 z -1$ (db)
Kauffman polynomial	$- z 9 a -1 - z 9 a -3 -4 z 8 a -2 -3 z 8 a -4 - z 8 + 3 z 7 a -1 - z 7 a -3 -4 z 7 a -5 + 13 z 6 a -2 + 7 z 6 a -4 -3 z 6 a -6 + 3 z 6 -3 a z 5 -8 z 5 a -1 + 6 z 5 a -3 + 10 z 5 a -5 - z 5 a -7 - a 2 z 4 -20 z 4 a -2 -6 z 4 a -4 + 7 z 4 a -6 -8 z 4 + 6 a z 3 + 6 z 3 a -1 -8 z 3 a -3 -6 z 3 a -5 + 2 z 3 a -7 + 2 a 2 z 2 + 8 z 2 a -2 + 2 z 2 a -4 -2 z 2 a -6 + 6 z 2 -2 a z -2 z a -1 + 2 z a -3 + 2 z a -5 + 1- a z -1 - a -1 z -1$ (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 L11n216. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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