L11a266

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_12,4,13,3 X_22,12,9,11 X_2,9,3,10 X_4,22,5,21 X_14,6,15,5 X_16,20,17,19 X_18,8,19,7 X_6,18,7,17 X_20,16,21,15 X_8,14,1,13
Gauss code	{1, -4, 2, -5, 6, -9, 8, -11}, {4, -1, 3, -2, 11, -6, 10, -7, 9, -8, 7, -10, 5, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-\frac{2 t(2)^2 t(1)^3-3 t(2) t(1)^3+t(1)^3+2 t(2)^3 t(1)^2-9 t(2)^2 t(1)^2+9 t(2) t(1)^2-3 t(1)^2-3 t(2)^3 t(1)+9 t(2)^2 t(1)-9 t(2) t(1)+2 t(1)+t(2)^3-3 t(2)^2+2 t(2)}{t(1)^{3/2} t(2)^{3/2}}$ (db)
Jones polynomial	$18 q^{9/2}-16 q^{7/2}+11 q^{5/2}-7 q^{3/2}+q^{21/2}-4 q^{19/2}+8 q^{17/2}-12 q^{15/2}+16 q^{13/2}-19 q^{11/2}+3 \sqrt{q}-\frac{1}{\sqrt{q}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$z 3 a -9 - z 5 a -7 + z a -7 -2 z 5 a -5 -3 z 3 a -5 -2 z a -5 - a -5 z -1 - z 5 a -3 + 2 z a -3 + a -3 z -1 + z 3 a -1 + z a -1$ (db)
Kauffman polynomial	$z 6 a -12 -2 z 4 a -12 + z 2 a -12 + 4 z 7 a -11 -10 z 5 a -11 + 6 z 3 a -11 - z a -11 + 6 z 8 a -10 -14 z 6 a -10 + 7 z 4 a -10 + 4 z 9 a -9 - z 7 a -9 -15 z 5 a -9 + 13 z 3 a -9 -3 z a -9 + z 10 a -8 + 11 z 8 a -8 -28 z 6 a -8 + 17 z 4 a -8 -2 z 2 a -8 + 7 z 9 a -7 -4 z 7 a -7 -16 z 5 a -7 + 19 z 3 a -7 -5 z a -7 + z 10 a -6 + 10 z 8 a -6 -20 z 6 a -6 + 12 z 4 a -6 - z 2 a -6 + 3 z 9 a -5 + 6 z 7 a -5 -20 z 5 a -5 + 20 z 3 a -5 -8 z a -5 + a -5 z -1 + 5 z 8 a -4 -4 z 6 a -4 - z 4 a -4 + 2 z 2 a -4 - a -4 + 5 z 7 a -3 -8 z 5 a -3 + 6 z 3 a -3 -4 z a -3 + a -3 z -1 + 3 z 6 a -2 -5 z 4 a -2 + 2 z 2 a -2 + z 5 a -1 -2 z 3 a -1 + z a -1$ (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 =

3 is the signature of L11a266. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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