L11a446

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,4,15,3 X_18,9,19,10 X_16,8,17,7 X_22,17,13,18 X_20,11,21,12 X_8,14,9,13 X_10,19,11,20 X_12,21,5,22 X₂₅₃₆ X_4,16,1,15
Gauss code	{1, -10, 2, -11}, {10, -1, 4, -7, 3, -8, 6, -9}, {7, -2, 11, -4, 5, -3, 8, -6, 9, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 3 u 3 - v 2 u 3 - v 3 w u 3 + 2 v 2 w u 3 - v w u 3 -2 v 3 u 2 + 4 v 2 u 2 -2 v u 2 + v 3 w u 2 -4 v 2 w u 2 + 3 v w u 2 - w u 2 + v 3 u -3 v 2 u + 4 v u + 2 v 2 w u -4 v w u + 2 w u - u + v 2 -2 v + v w - w + 1$ (db)
Jones polynomial	$q 3 -3 q 2 + 6 q -8 + 13 q -1 -14 q -2 + 15 q -3 -12 q -4 + 10 q -5 -6 q -6 + 3 q -7 - q -8$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$- a 2 z 8 + 2 a 4 z 6 -6 a 2 z 6 + z 6 - a 6 z 4 + 9 a 4 z 4 -14 a 2 z 4 + 4 z 4 -3 a 6 z 2 + 13 a 4 z 2 -16 a 2 z 2 + 5 z 2 -2 a 6 + 7 a 4 -9 a 2 + 4 + a 4 z -2 -2 a 2 z -2 + z -2$ (db)
Kauffman polynomial	$a 4 z 10 + a 2 z 10 + 3 a 5 z 9 + 7 a 3 z 9 + 4 a z 9 + 4 a 6 z 8 + 7 a 4 z 8 + 8 a 2 z 8 + 5 z 8 + 4 a 7 z 7 -2 a 5 z 7 -20 a 3 z 7 -11 a z 7 + 3 z 7 a -1 + 3 a 8 z 6 -4 a 6 z 6 -29 a 4 z 6 -41 a 2 z 6 + z 6 a -2 -18 z 6 + a 9 z 5 -5 a 7 z 5 -3 a 5 z 5 + 19 a 3 z 5 + 7 a z 5 -9 z 5 a -1 -6 a 8 z 4 -2 a 6 z 4 + 47 a 4 z 4 + 67 a 2 z 4 -3 z 4 a -2 + 21 z 4 -2 a 9 z 3 -2 a 7 z 3 + 6 a 5 z 3 + 4 a 3 z 3 + 2 a z 3 + 4 z 3 a -1 + 3 a 8 z 2 + a 6 z 2 -31 a 4 z 2 -44 a 2 z 2 + z 2 a -2 -14 z 2 + a 9 z + a 7 z -3 a 5 z -8 a 3 z -5 a z - a 8 + 9 a 4 + 13 a 2 + 6 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 =

-2 is the signature of L11a446. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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