L11a246

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 5 + v u 5 - v 3 u 4 + 5 v 2 u 4 -5 v u 4 + u 4 + 3 v 3 u 3 -9 v 2 u 3 + 10 v u 3 -3 u 3 -3 v 3 u 2 + 10 v 2 u 2 -9 v u 2 + 3 u 2 + v 3 u -5 v 2 u + 5 v u - u + v 2 - v$ (db)
Jones polynomial	$-q^{7/2}+5 q^{5/2}-11 q^{3/2}+17 \sqrt{q}-\frac{23}{\sqrt{q}}+\frac{25}{q^{3/2}}-\frac{25}{q^{5/2}}+\frac{21}{q^{7/2}}-\frac{15}{q^{9/2}}+\frac{8}{q^{11/2}}-\frac{4}{q^{13/2}}+\frac{1}{q^{15/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a 3 z 7 + a z 7 - a 5 z 5 + 3 a 3 z 5 + 2 a z 5 - z 5 a -1 -2 a 5 z 3 + 3 a 3 z 3 - a z 3 - z 3 a -1 -3 a z + z a -1 + a 5 z -1 - a 3 z -1$ (db)
Kauffman polynomial	$-3 a 4 z 10 -3 a 2 z 10 -7 a 5 z 9 -16 a 3 z 9 -9 a z 9 -7 a 6 z 8 -9 a 4 z 8 -15 a 2 z 8 -13 z 8 -4 a 7 z 7 + 12 a 5 z 7 + 30 a 3 z 7 + 3 a z 7 -11 z 7 a -1 - a 8 z 6 + 17 a 6 z 6 + 32 a 4 z 6 + 36 a 2 z 6 -5 z 6 a -2 + 17 z 6 + 10 a 7 z 5 -3 a 5 z 5 -17 a 3 z 5 + 12 a z 5 + 15 z 5 a -1 - z 5 a -3 + 2 a 8 z 4 -13 a 6 z 4 -29 a 4 z 4 -21 a 2 z 4 + 4 z 4 a -2 -3 z 4 -6 a 7 z 3 -6 a 5 z 3 + a 3 z 3 -3 a z 3 -4 z 3 a -1 + 3 a 6 z 2 + 7 a 4 z 2 + 4 a 2 z 2 + 4 a 5 z + 3 a 3 z -2 a z - z a -1 + a 4 - a 5 z -1 - a 3 z -1$ (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 L11a246. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -4$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{6}$
$r = -3$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -2$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = -1$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = 0$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{13}$
$r = 1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$