L11a389

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 - v w u 3 + w u 3 - u 3 -8 v u 2 + 5 v w u 2 -6 w u 2 + 5 u 2 + 6 v u -5 v w u + 8 w u -5 u - v + v w -2 w + 1$ (db)
Jones polynomial	$- q 5 + 4 q 4 -8 q 3 + 14 q 2 -17 q + 19-18 q -1 + 16 q -2 -10 q -3 + 6 q -4 -2 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 6 z -2 + a 6 -3 z 2 a 4 -3 a 4 z -2 -5 a 4 + 3 z 4 a 2 + 6 z 2 a 2 + 4 a 2 z -2 + 8 a 2 - z 6 -2 z 4 -5 z 2 -3 z -2 -6 + 2 z 4 a -2 + 2 z 2 a -2 + a -2 z -2 + 2 a -2 - z 2 a -4$ (db)
Kauffman polynomial	$a 2 z 10 + z 10 + 2 a 3 z 9 + 6 a z 9 + 4 z 9 a -1 + 2 a 4 z 8 + 5 a 2 z 8 + 7 z 8 a -2 + 10 z 8 + 2 a 5 z 7 + 3 a 3 z 7 - a z 7 + 5 z 7 a -1 + 7 z 7 a -3 + a 6 z 6 + 2 a 4 z 6 - a 2 z 6 -5 z 6 a -2 + 4 z 6 a -4 -11 z 6 -5 a 5 z 5 -12 a 3 z 5 -11 a z 5 -15 z 5 a -1 -10 z 5 a -3 + z 5 a -5 -4 a 6 z 4 -18 a 4 z 4 -26 a 2 z 4 -7 z 4 a -2 -6 z 4 a -4 -13 z 4 + 3 a 5 z 3 + 8 a 3 z 3 + 5 a z 3 + 5 z 3 a -1 + 4 z 3 a -3 - z 3 a -5 + 6 a 6 z 2 + 25 a 4 z 2 + 38 a 2 z 2 + 8 z 2 a -2 + 3 z 2 a -4 + 24 z 2 + a 5 z + a 3 z + a z + z a -1 -4 a 6 -14 a 4 -21 a 2 -4 a -2 -14- a 5 z -1 - a 3 z -1 - a z -1 - a -1 z -1 + a 6 z -2 + 3 a 4 z -2 + 4 a 2 z -2 + a -2 z -2 + 3 z -2$ (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 =

0 is the signature of L11a389. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2$	${\mathbb Z}^{2}$
$r = -3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -2$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = -1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 0$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{11}$
$r = 1$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 2$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$