L11a506

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 3 - v 2 w 2 u 3 + v w 2 u 3 + 2 v u 3 + 2 v 2 w u 3 -3 v w u 3 + w u 3 - u 3 + 2 v 2 u 2 + 2 v 2 w 2 u 2 -3 v w 2 u 2 + w 2 u 2 -4 v u 2 -4 v 2 w u 2 + 6 v w u 2 -3 w u 2 + 2 u 2 - v 2 u -2 v 2 w 2 u + 4 v w 2 u -2 w 2 u + 3 v u + 3 v 2 w u -6 v w u + 4 w u -2 u + v 2 w 2 -2 v w 2 + w 2 - v - v 2 w + 3 v w -2 w + 1$ (db)
Jones polynomial	$q 7 -4 q 6 + 9 q 5 -16 q 4 + 22 q 3 -24 q 2 + 26 q -21 + 17 q -1 -10 q -2 + 5 q -3 - q -4$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$- z 8 a -2 -5 z 6 a -2 + z 6 a -4 + 2 z 6 - a 2 z 4 -10 z 4 a -2 + 3 z 4 a -4 + 6 z 4 - a 2 z 2 -7 z 2 a -2 + 3 z 2 a -4 + 4 z 2 + a 2 + a -2 -2 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$4 z 10 a -2 + 4 z 10 + 8 a z 9 + 21 z 9 a -1 + 13 z 9 a -3 + 5 a 2 z 8 + 19 z 8 a -2 + 18 z 8 a -4 + 6 z 8 + a 3 z 7 -23 a z 7 -56 z 7 a -1 -17 z 7 a -3 + 15 z 7 a -5 -15 a 2 z 6 -77 z 6 a -2 -34 z 6 a -4 + 9 z 6 a -6 -49 z 6 -2 a 3 z 5 + 16 a z 5 + 34 z 5 a -1 -8 z 5 a -3 -20 z 5 a -5 + 4 z 5 a -7 + 13 a 2 z 4 + 71 z 4 a -2 + 24 z 4 a -4 -6 z 4 a -6 + z 4 a -8 + 53 z 4 + a 3 z 3 - a z 3 -2 z 3 a -1 + 10 z 3 a -3 + 9 z 3 a -5 - z 3 a -7 -2 a 2 z 2 -21 z 2 a -2 -8 z 2 a -4 + z 2 a -6 -14 z 2 + 2 a z + 2 z a -1 -2 a 2 -2 a -2 -3-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 L11a506. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 1$	$i = 3$
$r = -5$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{7}$
$r = -1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 0$	${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{13}$
$r = 1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = 2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{12}$
$r = 3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 5$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 6$	${\mathbb Z}_2$	${\mathbb Z}$