L11n383

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,7,15,8 X_4,15,1,16 X_10,6,11,5 X₈₄₉₃ X_17,22,18,19 X_11,20,12,21 X_19,12,20,13 X_21,18,22,5 X_16,10,17,9 X_2,14,3,13
Gauss code	{1, -11, 5, -3}, {-8, 7, -9, 6}, {4, -1, 2, -5, 10, -4, -7, 8, 11, -2, 3, -10, -6, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 + u 5 + 2 v u 4 -2 u 4 - v u 3 + u 3 - v w u 2 + w u 2 + 2 v w u -2 w u - v w + w$ (db)
Jones polynomial	$q 2 -2 q + 3-4 q -1 + 6 q -2 -4 q -3 + 5 q -4 -3 q -5 + 3 q -6 - q -7$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 2 a 6 + a 6 z -2 - a 6 + 2 z 4 a 4 + 6 z 2 a 4 -2 a 4 z -2 + 2 a 4 - z 6 a 2 -5 z 4 a 2 -8 z 2 a 2 + a 2 z -2 -3 a 2 + z 4 + 3 z 2 + 2$ (db)
Kauffman polynomial	$2 a 5 z 9 + 2 a 3 z 9 + 3 a 6 z 8 + 7 a 4 z 8 + 4 a 2 z 8 + a 7 z 7 -7 a 5 z 7 -6 a 3 z 7 + 2 a z 7 -15 a 6 z 6 -36 a 4 z 6 -21 a 2 z 6 -4 a 7 z 5 - a 5 z 5 -5 a 3 z 5 -8 a z 5 + 20 a 6 z 4 + 53 a 4 z 4 + 36 a 2 z 4 + 3 z 4 + 3 a 7 z 3 + 11 a 5 z 3 + 17 a 3 z 3 + 11 a z 3 + 2 z 3 a -1 -8 a 6 z 2 -27 a 4 z 2 -26 a 2 z 2 + z 2 a -2 -6 z 2 - a 7 z - a 5 z -5 a 3 z -7 a z -2 z a -1 - a 6 + 2 a 4 + 5 a 2 + 3-2 a 5 z -1 -2 a 3 z -1 + a 6 z -2 + 2 a 4 z -2 + a 2 z -2$ (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 =

0 is the signature of L11n383. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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