L11a202

(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 X₆₇₁₈ X_18,11,19,12 X_16,6,17,5 X_4,18,5,17 X_20,13,21,14 X_22,15,7,16 X_12,19,13,20 X_14,21,15,22
Gauss code	{1, -2, 3, -7, 6, -4}, {4, -1, 2, -3, 5, -10, 8, -11, 9, -6, 7, -5, 10, -8, 11, -9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 6 + v u 6 + v 2 u 5 - v u 5 + u 5 - v 2 u 4 + v u 4 - u 4 + v 2 u 3 - v u 3 + u 3 - v 2 u 2 + v u 2 - u 2 + v 2 u - v u + u + v -1$ (db)
Jones polynomial	$-\frac{1}{q^{3/2}}+\frac{1}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{3}{q^{9/2}}-\frac{5}{q^{11/2}}+\frac{5}{q^{13/2}}-\frac{5}{q^{15/2}}+\frac{5}{q^{17/2}}-\frac{4}{q^{19/2}}+\frac{3}{q^{21/2}}-\frac{2}{q^{23/2}}+\frac{1}{q^{25/2}}$ (db)
Signature	-7 (db)
HOMFLY-PT polynomial	$- z 7 a 9 -6 z 5 a 9 -11 z 3 a 9 -7 z a 9 -2 a 9 z -1 + z 9 a 7 + 8 z 7 a 7 + 23 z 5 a 7 + 30 z 3 a 7 + 19 z a 7 + 5 a 7 z -1 - z 7 a 5 -7 z 5 a 5 -16 z 3 a 5 -13 z a 5 -3 a 5 z -1$ (db)
Kauffman polynomial	$- z 2 a 16 -2 z 3 a 15 -3 z 4 a 14 + 2 z 2 a 14 -4 z 5 a 13 + 6 z 3 a 13 -5 z 6 a 12 + 13 z 4 a 12 -6 z 2 a 12 + a 12 -5 z 7 a 11 + 17 z 5 a 11 -13 z 3 a 11 + 3 z a 11 -4 z 8 a 10 + 15 z 6 a 10 -11 z 4 a 10 - z 2 a 10 -3 z 9 a 9 + 14 z 7 a 9 -18 z 5 a 9 + 9 z 3 a 9 -6 z a 9 + 2 a 9 z -1 - z 10 a 8 + 2 z 8 a 8 + 11 z 6 a 8 -31 z 4 a 8 + 22 z 2 a 8 -5 a 8 -4 z 9 a 7 + 27 z 7 a 7 -62 z 5 a 7 + 59 z 3 a 7 -25 z a 7 + 5 a 7 z -1 - z 10 a 6 + 6 z 8 a 6 -9 z 6 a 6 -4 z 4 a 6 + 14 z 2 a 6 -5 a 6 - z 9 a 5 + 8 z 7 a 5 -23 z 5 a 5 + 29 z 3 a 5 -16 z a 5 + 3 a 5 z -1$ (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 =

-7 is the signature of L11a202. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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