L11n149

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_9,19,10,18 X₆₇₁₈ X_22,19,7,20 X_12,5,13,6 X_3,10,4,11 X_4,15,5,16 X_16,12,17,11 X_20,13,21,14 X_14,21,15,22 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 $u$ , $v$ , $w$ , ...)	$v u 4 - u 4 -3 v u 3 + 2 u 3 -2 v 2 u 2 + 3 v u 2 -2 u 2 + 2 v 2 u -3 v u - v 2 + v$ (db)
Jones polynomial	$-\frac{1}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{5}{q^{7/2}}+\frac{6}{q^{9/2}}-\frac{7}{q^{11/2}}+\frac{7}{q^{13/2}}-\frac{6}{q^{15/2}}+\frac{4}{q^{17/2}}-\frac{3}{q^{19/2}}+\frac{1}{q^{21/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- z 3 a 9 - z a 9 + z 5 a 7 + 3 z 3 a 7 + 4 z a 7 + a 7 z -1 -3 z 3 a 5 -5 z a 5 - a 5 z -1 - z 3 a 3 - z a 3$ (db)
Kauffman polynomial	$- z 6 a 12 + 3 z 4 a 12 - z 2 a 12 -3 z 7 a 11 + 11 z 5 a 11 -9 z 3 a 11 + z a 11 -3 z 8 a 10 + 10 z 6 a 10 -7 z 4 a 10 + z 2 a 10 - z 9 a 9 - z 7 a 9 + 12 z 5 a 9 -13 z 3 a 9 + 4 z a 9 -4 z 8 a 8 + 13 z 6 a 8 -14 z 4 a 8 + 6 z 2 a 8 - z 9 a 7 + 2 z 7 a 7 -3 z 5 a 7 + 3 z 3 a 7 -3 z a 7 + a 7 z -1 - z 8 a 6 + 2 z 6 a 6 -6 z 4 a 6 + 5 z 2 a 6 - a 6 -4 z 5 a 5 + 6 z 3 a 5 -5 z a 5 + a 5 z -1 -2 z 4 a 4 + z 2 a 4 - z 3 a 3 + z a 3$ (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 =

-3 is the signature of L11n149. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -4$	$i = -2$
$r = -9$	${\mathbb Z}$
$r = -8$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -7$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -6$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{3}$
$r = -5$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -2$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -1$	${\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 0$	${\mathbb Z}$	${\mathbb Z}$