L11n152

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_18,9,19,10 X₆₇₁₈ X_19,7,20,22 X_12,5,13,6 X_10,4,11,3 X_4,15,5,16 X_16,12,17,11 X_13,21,14,20 X_21,15,22,14 X_2,18,3,17
Gauss code	{1, -11, 6, -7, 5, -3}, {3, -1, 2, -6, 8, -5, -9, 10, 7, -8, 11, -2, -4, 9, -10, 4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 4 - u 4 -3 v u 3 + 2 u 3 - v 2 u 2 + 3 v u 2 - u 2 + 2 v 2 u -3 v u - v 2 + v$ (db)
Jones polynomial	$2 q^{7/2}-4 q^{5/2}+5 q^{3/2}-7 \sqrt{q}+\frac{6}{\sqrt{q}}-\frac{6}{q^{3/2}}+\frac{4}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$a z 5 - a 3 z 3 + 3 a z 3 -3 z 3 a -1 - a 3 z + 4 a z -6 z a -1 + 2 z a -3 + 2 a z -1 -3 a -1 z -1 + a -3 z -1$ (db)
Kauffman polynomial	$- a z 9 - z 9 a -1 -3 a 2 z 8 - z 8 a -2 -4 z 8 -3 a 3 z 7 - a z 7 + 2 z 7 a -1 - a 4 z 6 + 10 a 2 z 6 + 3 z 6 a -2 + 14 z 6 + 11 a 3 z 5 + 14 a z 5 + 2 z 5 a -1 - z 5 a -3 + 3 a 4 z 4 -6 a 2 z 4 -4 z 4 a -2 -13 z 4 -9 a 3 z 3 -18 a z 3 -11 z 3 a -1 -2 z 3 a -3 - a 4 z 2 -3 z 2 a -2 -2 z 2 a -4 + 2 a 3 z + 9 a z + 10 z a -1 + 3 z a -3 + 3 a -2 + a -4 + 3-2 a z -1 -3 a -1 z -1 - a -3 z -1$ (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 =

1 is the signature of L11n152. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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