L11n141

(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_2,17,3,18 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_19,4,20,5
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 $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + v 2 u 3 - v u 2 + u -2$ (db)
Jones polynomial	$-\frac{1}{q^{7/2}}+\frac{1}{q^{9/2}}-\frac{2}{q^{11/2}}+\frac{1}{q^{13/2}}-\frac{2}{q^{15/2}}+\frac{1}{q^{17/2}}-\frac{1}{q^{19/2}}+\frac{1}{q^{21/2}}$ (db)
Signature	-7 (db)
HOMFLY-PT polynomial	$- z a 13 - a 13 z -1 + z 5 a 11 + 6 z 3 a 11 + 8 z a 11 + 2 a 11 z -1 - z 7 a 9 -6 z 5 a 9 -10 z 3 a 9 -5 z a 9 - z 7 a 7 -6 z 5 a 7 -10 z 3 a 7 -5 z a 7 - a 7 z -1$ (db)
Kauffman polynomial	$z 2 a 14 -2 a 14 + z 3 a 13 -2 z a 13 + a 13 z -1 - z 8 a 12 + 7 z 6 a 12 -16 z 4 a 12 + 16 z 2 a 12 -5 a 12 - z 9 a 11 + 7 z 7 a 11 -17 z 5 a 11 + 20 z 3 a 11 -10 z a 11 + 2 a 11 z -1 -2 z 8 a 10 + 12 z 6 a 10 -21 z 4 a 10 + 14 z 2 a 10 -3 a 10 - z 9 a 9 + 6 z 7 a 9 -11 z 5 a 9 + 9 z 3 a 9 -3 z a 9 - z 8 a 8 + 5 z 6 a 8 -5 z 4 a 8 - z 2 a 8 + a 8 - z 7 a 7 + 6 z 5 a 7 -10 z 3 a 7 + 5 z a 7 - a 7 z -1$ (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 L11n141. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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