L11n264

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_14,7,15,8 X_8,13,5,14 X_18,12,19,11 X_19,22,20,9 X_15,20,16,21 X_21,16,22,17 X_12,18,13,17 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -10, 2, -11}, {10, -1, 3, -4}, {11, -2, 5, -9, 4, -3, -7, 8, 9, -5, -6, 7, -8, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 3 - v w u 3 + w u 3 - u 3 - v u 2 + 2 v w u 2 - w u 2 + u 2 + v u - v w u + w u -2 u - v + v w - w + 1$ (db)
Jones polynomial	$1-3 q -1 + 5 q -2 -5 q -3 + 7 q -4 -5 q -5 + 6 q -6 -3 q -7 + q -8$ (db)
Signature	-4 (db)
HOMFLY-PT polynomial	$a 8 z -2 + z 4 a 6 + z 2 a 6 -2 a 6 z -2 -3 a 6 - z 6 a 4 -3 z 4 a 4 + a 4 z -2 + 3 a 4 + z 4 a 2 + 2 z 2 a 2$ (db)
Kauffman polynomial	$2 z 3 a 9 + z 8 a 8 -5 z 6 a 8 + 11 z 4 a 8 -6 z 2 a 8 - a 8 z -2 + 3 a 8 + z 9 a 7 -3 z 7 a 7 + 2 z 5 a 7 + 3 z 3 a 7 -3 z a 7 + 2 a 7 z -1 + 4 z 8 a 6 -16 z 6 a 6 + 22 z 4 a 6 -14 z 2 a 6 -2 a 6 z -2 + 5 a 6 + z 9 a 5 -8 z 5 a 5 + 7 z 3 a 5 -3 z a 5 + 2 a 5 z -1 + 3 z 8 a 4 -10 z 6 a 4 + 8 z 4 a 4 -6 z 2 a 4 - a 4 z -2 + 3 a 4 + 3 z 7 a 3 -10 z 5 a 3 + 6 z 3 a 3 + z 6 a 2 -3 z 4 a 2 + 2 z 2 a 2$ (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 =

-4 is the signature of L11n264. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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