L11n425

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_16,8,17,7 X_5,14,6,15 X_3,10,4,11 X_13,4,14,5 X_17,2,18,3 X_9,19,10,18 X_21,7,22,12 X_11,13,12,22 X_20,16,21,15 X_6,19,1,20
Gauss code	{1, 6, -4, 5, -3, -11}, {2, -1, -7, 4, -9, 8}, {-5, 3, 10, -2, -6, 7, 11, -10, -8, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 3 - v 2 w u 3 + v w u 3 - v 2 u 2 + v u 2 + v 2 w u 2 -2 v w u 2 - v w 2 u + w 2 u + 2 v w u - w u + v w 2 - v w + w$ (db)
Jones polynomial	$2 q 2 -3 q + 5-5 q -1 + 6 q -2 -4 q -3 + 4 q -4 -2 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- a 2 z 6 + a 4 z 4 -5 a 2 z 4 + z 4 + 3 a 4 z 2 -9 a 2 z 2 + 2 z 2 + 3 a 4 -6 a 2 + a -2 + 2 + a 4 z -2 -2 a 2 z -2 + z -2$ (db)
Kauffman polynomial	$a 3 z 9 + a z 9 + 3 a 4 z 8 + 4 a 2 z 8 + z 8 + 2 a 5 z 7 - a 3 z 7 -3 a z 7 + a 6 z 6 -14 a 4 z 6 -19 a 2 z 6 -4 z 6 -7 a 5 z 5 -8 a 3 z 5 + z 5 a -1 -4 a 6 z 4 + 22 a 4 z 4 + 33 a 2 z 4 + 7 z 4 + 4 a 5 z 3 + 14 a 3 z 3 + 10 a z 3 + 3 a 6 z 2 -19 a 4 z 2 -27 a 2 z 2 + 2 z 2 a -2 -3 z 2 -9 a 3 z -9 a z + 7 a 4 + 11 a 2 -2 a -2 + 3 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 L11n425. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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