L11a149

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_2,9,3,10 X_10,3,11,4 X_14,17,15,18 X_16,7,17,8 X_22,15,7,16 X_18,13,19,14 X_6,20,1,19 X_20,12,21,11 X_12,6,13,5 X_4,21,5,22
Gauss code	{1, -2, 3, -11, 10, -8}, {5, -1, 2, -3, 9, -10, 7, -4, 6, -5, 4, -7, 8, -9, 11, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + 2 v u 4 + 5 v 2 u 3 -8 v u 3 + 2 u 3 -5 v 2 u 2 + 11 v u 2 -5 u 2 + 2 v 2 u -8 v u + 5 u + 2 v -2$ (db)
Jones polynomial	$q^{3/2}-3 \sqrt{q}+\frac{6}{\sqrt{q}}-\frac{12}{q^{3/2}}+\frac{15}{q^{5/2}}-\frac{19}{q^{7/2}}+\frac{19}{q^{9/2}}-\frac{17}{q^{11/2}}+\frac{13}{q^{13/2}}-\frac{8}{q^{15/2}}+\frac{4}{q^{17/2}}-\frac{1}{q^{19/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$z 5 a 7 + 2 z 3 a 7 - a 7 z -1 - z 7 a 5 -3 z 5 a 5 - z 3 a 5 + 4 z a 5 + 3 a 5 z -1 - z 7 a 3 -4 z 5 a 3 -7 z 3 a 3 -7 z a 3 -2 a 3 z -1 + z 5 a + 3 z 3 a + 2 z a$ (db)
Kauffman polynomial	$- z 5 a 11 + z 3 a 11 -4 z 6 a 10 + 6 z 4 a 10 - z 2 a 10 -7 z 7 a 9 + 11 z 5 a 9 -3 z 3 a 9 -8 z 8 a 8 + 13 z 6 a 8 -6 z 4 a 8 + a 8 -6 z 9 a 7 + 8 z 7 a 7 -5 z 5 a 7 + 2 z 3 a 7 - a 7 z -1 -2 z 10 a 6 -7 z 8 a 6 + 21 z 6 a 6 -18 z 4 a 6 + 3 a 6 -10 z 9 a 5 + 24 z 7 a 5 -24 z 5 a 5 + 6 z 3 a 5 + 5 z a 5 -3 a 5 z -1 -2 z 10 a 4 -3 z 8 a 4 + 13 z 6 a 4 -10 z 4 a 4 - z 2 a 4 + 3 a 4 -4 z 9 a 3 + 6 z 7 a 3 + 2 z 5 a 3 -8 z 3 a 3 + 8 z a 3 -2 a 3 z -1 -4 z 8 a 2 + 8 z 6 a 2 - z 4 a 2 -2 z 2 a 2 -3 z 7 a + 9 z 5 a -8 z 3 a + 3 z a - z 6 + 3 z 4 -2 z 2$ (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 =

-3 is the signature of L11a149. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -4$	$i = -2$
$r = -8$	${\mathbb Z}$
$r = -7$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -5$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -4$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -3$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -2$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{11}$
$r = -1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 0$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{8}$
$r = 1$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 2$	${\mathbb Z}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 3$	${\mathbb Z}_2$	${\mathbb Z}$