L11n387

(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_5,12,6,13 X₈₄₉₃ X_11,19,12,22 X_21,18,22,5 X_9,20,10,21 X_17,11,18,10 X_19,17,20,16 X_2,14,3,13
Gauss code	{1, -11, 5, -3}, {-10, 8, -7, 6}, {-4, -1, 2, -5, -8, 9, -6, 4, 11, -2, 3, 10, -9, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 3 - v w u 3 + w u 3 - u 3 -3 v u 2 + 3 v w u 2 -3 w u 2 + 3 u 2 + 3 v u -3 v w u + 3 w u -3 u - v + v w - w + 1$ (db)
Jones polynomial	$- q 3 + 4 q 2 -6 q + 11-10 q -1 + 11 q -2 -9 q -3 + 7 q -4 -4 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- a 2 z 6 + a 4 z 4 -3 a 2 z 4 + 2 z 4 + a 4 z 2 -3 a 2 z 2 - z 2 a -2 + 3 z 2 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$2 a 3 z 9 + 2 a z 9 + 5 a 4 z 8 + 9 a 2 z 8 + 4 z 8 + 4 a 5 z 7 + 3 a 3 z 7 + a z 7 + 2 z 7 a -1 + a 6 z 6 -13 a 4 z 6 -27 a 2 z 6 -13 z 6 -11 a 5 z 5 -23 a 3 z 5 -16 a z 5 -4 z 5 a -1 -2 a 6 z 4 + 5 a 4 z 4 + 25 a 2 z 4 + 4 z 4 a -2 + 22 z 4 + 6 a 5 z 3 + 20 a 3 z 3 + 23 a z 3 + 10 z 3 a -1 + z 3 a -3 + a 6 z 2 - a 4 z 2 -9 a 2 z 2 -4 z 2 a -2 -11 z 2 - a 5 z -4 a 3 z -6 a z -4 z a -1 - z a -3 + 1-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 L11n387. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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