L11n200

(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_5,14,6,15 X_16,7,17,8 X_20,15,21,16 X_13,18,14,19 X_6,22,7,21 X_22,18,9,17 X_19,5,20,4 X_2,9,3,10 X_8,11,1,12
Gauss code	{1, -10, 2, 9, -3, -7, 4, -11}, {10, -1, 11, -2, -6, 3, 5, -4, 8, 6, -9, -5, 7, -8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 3 + v u 3 - v 3 u 2 + 2 v 2 u 2 -3 v u 2 + u 2 + v 3 u -3 v 2 u + 2 v u - u + v 2 - v$ (db)
Jones polynomial	$\sqrt{q}-\frac{3}{\sqrt{q}}+\frac{4}{q^{3/2}}-\frac{6}{q^{5/2}}+\frac{5}{q^{7/2}}-\frac{6}{q^{9/2}}+\frac{5}{q^{11/2}}-\frac{3}{q^{13/2}}+\frac{2}{q^{15/2}}-\frac{1}{q^{17/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z 3 a 7 + 2 z a 7 - z 5 a 5 -3 z 3 a 5 -2 z a 5 + a 5 z -1 - z 5 a 3 -3 z 3 a 3 -3 z a 3 - a 3 z -1 + z 3 a + z a$ (db)
Kauffman polynomial	$- z 7 a 9 + 5 z 5 a 9 -7 z 3 a 9 + 2 z a 9 -2 z 8 a 8 + 10 z 6 a 8 -15 z 4 a 8 + 7 z 2 a 8 - z 9 a 7 + 2 z 7 a 7 + 4 z 5 a 7 -6 z 3 a 7 -4 z 8 a 6 + 16 z 6 a 6 -18 z 4 a 6 + 8 z 2 a 6 - z 9 a 5 + z 7 a 5 + 3 z 5 a 5 + z 3 a 5 - z a 5 - a 5 z -1 -2 z 8 a 4 + 5 z 6 a 4 -3 z 4 a 4 + z 2 a 4 + a 4 -2 z 7 a 3 + 4 z 5 a 3 -3 z 3 a 3 + 2 z a 3 - a 3 z -1 - z 6 a 2 - z 2 a 2 -3 z 3 a + z a - z 2$ (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 L11n200. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -8$	${\mathbb Z}$
$r = -7$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{4}$
$r = -3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -2$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -1$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 0$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}^{2}$
$r = 1$	${\mathbb Z}_2$	${\mathbb Z}$