L11n148

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_9,19,10,18 X₆₇₁₈ X_19,7,20,22 X_12,5,13,6 X_3,10,4,11 X_4,15,5,16 X_16,12,17,11 X_13,21,14,20 X_21,15,22,14 X_17,2,18,3
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 $u$ , $v$ , $w$ , ...)	$- v u 4 - u 4 + v u 3 - v u 2 + v u - v 2 - v$ (db)
Jones polynomial	$q^{5/2}-q^{3/2}+\sqrt{q}-\frac{2}{\sqrt{q}}+\frac{1}{q^{3/2}}-\frac{1}{q^{5/2}}-\frac{1}{q^{11/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z a 5 + a 5 z -1 - z 5 a -5 z 3 a -7 z a -2 a z -1 + z 3 a -1 + 3 z a -1 + a -1 z -1$ (db)
Kauffman polynomial	$- a 5 z 7 + a z 7 + a 2 z 6 + z 6 + 7 a 5 z 5 + a 3 z 5 -7 a z 5 - z 5 a -1 + a 4 z 4 -6 a 2 z 4 - z 4 a -2 -8 z 4 -14 a 5 z 3 -4 a 3 z 3 + 13 a z 3 + 3 z 3 a -1 -3 a 4 z 2 + 8 a 2 z 2 + 3 z 2 a -2 + 14 z 2 + 8 a 5 z + 2 a 3 z -9 a z -3 z a -1 + a 4 -3 a 2 -2 a -2 -5- a 5 z -1 + 2 a z -1 + a -1 z -1$ (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 L11n148. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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