L11n204

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_7,16,8,17 X_11,18,12,19 X_2,19,3,20 X_3,12,4,13 X_20,13,21,14 X_14,5,15,6 X_6,9,7,10 X_15,22,16,9 X_17,8,18,1 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 $u$ , $v$ , $w$ , ...)	$- v 3 u 5 - v 2 u 3 - v u 2 -1$ (db)
Jones polynomial	$-\frac{1}{q^{9/2}}-\frac{1}{q^{13/2}}+\frac{1}{q^{21/2}}-\frac{1}{q^{23/2}}$ (db)
Signature	-8 (db)
HOMFLY-PT polynomial	$- z 3 a 13 -3 z a 13 - a 13 z -1 + z 7 a 11 + 8 z 5 a 11 + 20 z 3 a 11 + 17 z a 11 + 3 a 11 z -1 - z 9 a 9 -9 z 7 a 9 -28 z 5 a 9 -36 z 3 a 9 -18 z a 9 -2 a 9 z -1$ (db)
Kauffman polynomial	$- z a 15 - a 14 + z 3 a 13 -3 z a 13 + a 13 z -1 - z 8 a 12 + 8 z 6 a 12 -20 z 4 a 12 + 17 z 2 a 12 -3 a 12 - z 9 a 11 + 9 z 7 a 11 -28 z 5 a 11 + 37 z 3 a 11 -20 z a 11 + 3 a 11 z -1 - z 8 a 10 + 8 z 6 a 10 -20 z 4 a 10 + 17 z 2 a 10 -3 a 10 - z 9 a 9 + 9 z 7 a 9 -28 z 5 a 9 + 36 z 3 a 9 -18 z a 9 + 2 a 9 z -1$ (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 =

-8 is the signature of L11n204. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -10$	$i = -8$	$i = -6$
$r = -8$		${\mathbb Z}$	${\mathbb Z}$
$r = -7$		${\mathbb Z}$
$r = -6$		${\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}$	${\mathbb Z}$
$r = -4$		${\mathbb Z}$	${\mathbb Z}$
$r = -3$	${\mathbb Z}$
$r = -2$	${\mathbb Z}_2$	${\mathbb Z}$
$r = -1$
$r = 0$	${\mathbb Z}$	${\mathbb Z}$