L11n202

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_16,8,17,7 X_11,18,12,19 X_19,3,20,2 X_3,12,4,13 X_13,21,14,20 X_5,15,6,14 X_6,9,7,10 X_15,22,16,9 X_8,18,1,17 X_21,4,22,5
Gauss code	{1, 4, -5, 11, -7, -8, 2, -10}, {8, -1, -3, 5, -6, 7, -9, -2, 10, 3, -4, 6, -11, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 3 u 3 + v 2 u 3 + v 3 u 2 -2 v 2 u 2 + v u 2 + v 2 u -2 v u + u + v -1$ (db)
Jones polynomial	$q^{7/2}-2 q^{5/2}+2 q^{3/2}-4 \sqrt{q}+\frac{3}{\sqrt{q}}-\frac{4}{q^{3/2}}+\frac{3}{q^{5/2}}-\frac{2}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{1}{q^{11/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- a z 7 + a 3 z 5 -6 a z 5 + z 5 a -1 + 4 a 3 z 3 -11 a z 3 + 4 z 3 a -1 + 3 a 3 z -6 a z + 3 z a -1 + a z -1 - a -1 z -1$ (db)
Kauffman polynomial	$- a 3 z 9 - a z 9 -2 a 4 z 8 -3 a 2 z 8 - z 8 - a 5 z 7 + 4 a 3 z 7 + 5 a z 7 + 11 a 4 z 6 + 15 a 2 z 6 + 4 z 6 + 5 a 5 z 5 -3 a 3 z 5 -11 a z 5 -3 z 5 a -1 -17 a 4 z 4 -22 a 2 z 4 -2 z 4 a -2 -7 z 4 -6 a 5 z 3 + a 3 z 3 + 15 a z 3 + 6 z 3 a -1 -2 z 3 a -3 + 7 a 4 z 2 + 11 a 2 z 2 + z 2 a -2 - z 2 a -4 + 6 z 2 + a 5 z -2 a 3 z -6 a z -2 z a -1 + z a -3 + 1- a z -1 - a -1 z -1$ (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 L11n202. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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