L11n430

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_9,20,10,21 X_14,5,15,6 X_12,14,7,13 X_16,8,17,7 X_22,18,13,17 X_3,10,4,11 X_18,11,19,12 X_6,15,1,16 X_4,20,5,19 X_21,3,22,2
Gauss code	{1, 11, -7, -10, 3, -9}, {5, -1, -2, 7, 8, -4}, {4, -3, 9, -5, 6, -8, 10, 2, -11, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 3 + v u 3 + v 2 w u 3 - v w u 3 + v 2 u 2 - v w 2 u 2 -2 v u 2 - v 2 w u 2 + 3 v w u 2 + 2 v w 2 u - w 2 u + v u -3 v w u + w u - v w 2 + w 2 + v w - w$ (db)
Jones polynomial	$- q 3 + 3 q 2 -5 q + 8-7 q -1 + 9 q -2 -6 q -3 + 5 q -4 -3 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- a 2 z 6 + a 4 z 4 -4 a 2 z 4 + 2 z 4 + 2 a 4 z 2 -6 a 2 z 2 - z 2 a -2 + 5 z 2 + a 4 -4 a 2 - a -2 + 4 + a 4 z -2 -2 a 2 z -2 + z -2$ (db)
Kauffman polynomial	$2 a 3 z 9 + 2 a z 9 + 4 a 4 z 8 + 7 a 2 z 8 + 3 z 8 + 3 a 5 z 7 -4 a 3 z 7 -6 a z 7 + z 7 a -1 + a 6 z 6 -15 a 4 z 6 -29 a 2 z 6 -13 z 6 -10 a 5 z 5 -3 a 3 z 5 + 6 a z 5 - z 5 a -1 -3 a 6 z 4 + 16 a 4 z 4 + 43 a 2 z 4 + 3 z 4 a -2 + 27 z 4 + 6 a 5 z 3 + 5 a 3 z 3 + 2 a z 3 + 4 z 3 a -1 + z 3 a -3 + a 6 z 2 -9 a 4 z 2 -27 a 2 z 2 -4 z 2 a -2 -21 z 2 -2 a 3 z -4 a z -3 z a -1 - z a -3 + 3 a 4 + 7 a 2 + 2 a -2 + 7 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 L11n430. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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