L11a244

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + 2 v u 4 + 5 v 2 u 3 -11 v u 3 + 6 u 3 -9 v 2 u 2 + 19 v u 2 -9 u 2 + 6 v 2 u -11 v u + 5 u + 2 v -1$ (db)
Jones polynomial	$q^{9/2}-5 q^{7/2}+11 q^{5/2}-18 q^{3/2}+25 \sqrt{q}-\frac{28}{\sqrt{q}}+\frac{28}{q^{3/2}}-\frac{25}{q^{5/2}}+\frac{17}{q^{7/2}}-\frac{11}{q^{9/2}}+\frac{4}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 -2 a 3 z 5 + 3 a z 5 -2 z 5 a -1 + a 5 z 3 -4 a 3 z 3 + 6 a z 3 -3 z 3 a -1 + z 3 a -3 + a 5 z -6 a 3 z + 4 a z -2 z a -1 + 2 a 5 z -1 -3 a 3 z -1 + a z -1$ (db)
Kauffman polynomial	$-3 a 2 z 10 -3 z 10 -10 a 3 z 9 -19 a z 9 -9 z 9 a -1 -13 a 4 z 8 -24 a 2 z 8 -10 z 8 a -2 -21 z 8 -10 a 5 z 7 + 3 a 3 z 7 + 26 a z 7 + 8 z 7 a -1 -5 z 7 a -3 -4 a 6 z 6 + 18 a 4 z 6 + 62 a 2 z 6 + 21 z 6 a -2 - z 6 a -4 + 62 z 6 - a 7 z 5 + 16 a 5 z 5 + 17 a 3 z 5 + 5 a z 5 + 14 z 5 a -1 + 9 z 5 a -3 + 3 a 6 z 4 -8 a 4 z 4 -46 a 2 z 4 -13 z 4 a -2 + z 4 a -4 -49 z 4 + a 7 z 3 -15 a 5 z 3 -16 a 3 z 3 -9 a z 3 -13 z 3 a -1 -4 z 3 a -3 -3 a 4 z 2 + 9 a 2 z 2 + 2 z 2 a -2 + 14 z 2 + 8 a 5 z + 7 a 3 z + z a -1 + 3 a 4 + 3 a 2 + 1-2 a 5 z -1 -3 a 3 z -1 - a z -1$ (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 L11a244. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -6$	${\mathbb Z}$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{4}$
$r = -4$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -3$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -2$	${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = -1$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{15}$	${\mathbb Z}^{15}$
$r = 0$	${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{14}$
$r = 1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{14}$	${\mathbb Z}^{14}$
$r = 2$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 3$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$