L11n140

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_18,11,19,12 X_3,10,4,11 X_17,3,18,2 X_12,5,13,6 X₆₇₁₈ X_9,16,10,17 X_15,20,16,21 X_13,22,14,7 X_21,14,22,15 X_4,20,5,19
Gauss code	{1, 4, -3, -11, 5, -6}, {6, -1, -7, 3, 2, -5, -9, 10, -8, 7, -4, -2, 11, 8, -10, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 2 + 3 v u 2 + v 2 u -5 v u + u + 3 v -1$ (db)
Jones polynomial	$-\frac{2}{q^{3/2}}+\frac{3}{q^{5/2}}-\frac{5}{q^{7/2}}+\frac{5}{q^{9/2}}-\frac{6}{q^{11/2}}+\frac{4}{q^{13/2}}-\frac{3}{q^{15/2}}+\frac{2}{q^{17/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 9 z -1 - z 3 a 7 + 2 a 7 z -1 + z 5 a 5 + 3 z 3 a 5 + 3 z a 5 -2 z 3 a 3 -4 z a 3 - a 3 z -1$ (db)
Kauffman polynomial	$-3 z 4 a 10 + 7 z 2 a 10 -2 a 10 - z 7 a 9 + z 5 a 9 + 2 z 3 a 9 -2 z a 9 + a 9 z -1 - z 8 a 8 + 3 z 6 a 8 -9 z 4 a 8 + 13 z 2 a 8 -5 a 8 -3 z 7 a 7 + 7 z 5 a 7 -6 z 3 a 7 -2 z a 7 + 2 a 7 z -1 - z 8 a 6 + 2 z 6 a 6 -6 z 4 a 6 + 6 z 2 a 6 -3 a 6 -2 z 7 a 5 + 6 z 5 a 5 -11 z 3 a 5 + 5 z a 5 - z 6 a 4 + a 4 -3 z 3 a 3 + 5 z a 3 - a 3 z -1$ (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 =

-3 is the signature of L11n140. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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