L11n295

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,4,13,3 X_20,16,21,15 X_14,8,15,7 X_21,10,22,5 X_11,19,12,18 X_9,17,10,16 X_17,11,18,22 X_8,19,9,20 X₂₅₃₆ X_4,14,1,13
Gauss code	{1, -10, 2, -11}, {10, -1, 4, -9, -7, 5}, {-6, -2, 11, -4, 3, 7, -8, 6, 9, -3, -5, 8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 2 -2 v u 2 - v 2 w u 2 + 3 v w u 2 - w u 2 -2 v 2 u + 4 v u + v 2 w u -4 v w u + 2 w u - u + v 2 -3 v + 2 v w - w + 1$ (db)
Jones polynomial	$- q 8 + 3 q 7 -6 q 6 + 8 q 5 -10 q 4 + 11 q 3 -8 q 2 + 8 q -3 + 2 q -1$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$z 6 a -4 -3 z 4 a -2 + 4 z 4 a -4 - z 4 a -6 -9 z 2 a -2 + 8 z 2 a -4 -2 z 2 a -6 + 2 z 2 -10 a -2 + 8 a -4 -2 a -6 + 4-5 a -2 z -2 + 4 a -4 z -2 - a -6 z -2 + 2 z -2$ (db)
Kauffman polynomial	$z 9 a -3 + z 9 a -5 + 2 z 8 a -2 + 6 z 8 a -4 + 4 z 8 a -6 + z 7 a -1 + 2 z 7 a -3 + 6 z 7 a -5 + 5 z 7 a -7 -6 z 6 a -2 -18 z 6 a -4 -9 z 6 a -6 + 3 z 6 a -8 - z 5 a -1 -10 z 5 a -3 -23 z 5 a -5 -13 z 5 a -7 + z 5 a -9 + 18 z 4 a -2 + 30 z 4 a -4 + 9 z 4 a -6 -6 z 4 a -8 + 3 z 4 + 5 z 3 a -1 + 24 z 3 a -3 + 32 z 3 a -5 + 11 z 3 a -7 -2 z 3 a -9 -25 z 2 a -2 -24 z 2 a -4 -6 z 2 a -6 + z 2 a -8 -8 z 2 -11 z a -1 -24 z a -3 -18 z a -5 -5 z a -7 + 15 a -2 + 12 a -4 + 3 a -6 + 7 + 5 a -1 z -1 + 9 a -3 z -1 + 5 a -5 z -1 + a -7 z -1 -5 a -2 z -2 -4 a -4 z -2 - a -6 z -2 -2 z -2$ (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 =

2 is the signature of L11n295. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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