L11a148

(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_20,11,21,12 X_12,6,13,5 X_4,20,5,19 X_14,18,15,17 X_16,8,17,7 X_22,16,7,15 X_18,14,19,13 X_6,21,1,22
Gauss code	{1, -2, 3, -6, 5, -11}, {8, -1, 2, -3, 4, -5, 10, -7, 9, -8, 7, -10, 6, -4, 11, -9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + 2 v u 4 + 5 v 2 u 3 -6 v u 3 + 2 u 3 -5 v 2 u 2 + 9 v u 2 -5 u 2 + 2 v 2 u -6 v u + 5 u + 2 v -2$ (db)
Jones polynomial	$-q^{11/2}+4 q^{9/2}-7 q^{7/2}+11 q^{5/2}-15 q^{3/2}+16 \sqrt{q}-\frac{17}{\sqrt{q}}+\frac{14}{q^{3/2}}-\frac{11}{q^{5/2}}+\frac{6}{q^{7/2}}-\frac{3}{q^{9/2}}+\frac{1}{q^{11/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 + z 7 a -1 - a 3 z 5 + 4 a z 5 + 3 z 5 a -1 - z 5 a -3 -3 a 3 z 3 + 6 a z 3 -2 z 3 a -3 -2 a 3 z + 5 a z -5 z a -1 + z a -3 + 2 a z -1 -3 a -1 z -1 + a -3 z -1$ (db)
Kauffman polynomial	$-2 z 10 a -2 -2 z 10 -5 a z 9 -10 z 9 a -1 -5 z 9 a -3 -7 a 2 z 8 -3 z 8 a -2 -4 z 8 a -4 -6 z 8 -7 a 3 z 7 + 3 a z 7 + 28 z 7 a -1 + 17 z 7 a -3 - z 7 a -5 -5 a 4 z 6 + 9 a 2 z 6 + 26 z 6 a -2 + 15 z 6 a -4 + 25 z 6 -3 a 5 z 5 + 9 a 3 z 5 + 12 a z 5 -18 z 5 a -1 -15 z 5 a -3 + 3 z 5 a -5 - a 6 z 4 + 4 a 4 z 4 -2 a 2 z 4 -25 z 4 a -2 -15 z 4 a -4 -17 z 4 + 3 a 5 z 3 -6 a 3 z 3 -15 a z 3 - z 3 a -1 + 3 z 3 a -3 -2 z 3 a -5 + a 6 z 2 - a 4 z 2 -2 a 2 z 2 + 2 z 2 a -2 + 2 z 2 a -4 - a 5 z + a 3 z + 8 a z + 7 z a -1 + z a -3 + 3 a -2 + a -4 + 3-2 a z -1 -3 a -1 z -1 - a -3 z -1$ (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 L11a148. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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