L11n146

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_9,19,10,18 X₆₇₁₈ X_19,7,20,22 X_5,13,6,12 X_3,10,4,11 X_15,5,16,4 X_11,16,12,17 X_13,21,14,20 X_21,15,22,14 X_17,2,18,3
Gauss code	{1, 11, -6, 7, -5, -3}, {3, -1, -2, 6, -8, 5, -9, 10, -7, 8, -11, 2, -4, 9, -10, 4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 4 + u 4 - v 2 u 3 + 4 v u 3 -2 u 3 + 2 v 2 u 2 -5 v u 2 + 2 u 2 -2 v 2 u + 4 v u - u + v 2 - v$ (db)
Jones polynomial	$-q^{9/2}+4 q^{7/2}-6 q^{5/2}+8 q^{3/2}-10 \sqrt{q}+\frac{8}{\sqrt{q}}-\frac{8}{q^{3/2}}+\frac{5}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$a z 5 + z 5 a -1 - a 3 z 3 + 2 a z 3 + z 3 a -1 - z 3 a -3 - a 3 z + 2 a z -2 z a -1 + 2 a z -1 -3 a -1 z -1 + a -3 z -1$ (db)
Kauffman polynomial	$- a z 9 - z 9 a -1 -3 a 2 z 8 -2 z 8 a -2 -5 z 8 -3 a 3 z 7 -4 a z 7 -2 z 7 a -1 - z 7 a -3 - a 4 z 6 + 7 a 2 z 6 + 3 z 6 a -2 + 11 z 6 + 10 a 3 z 5 + 19 a z 5 + 7 z 5 a -1 -2 z 5 a -3 + 3 a 4 z 4 -5 z 4 a -2 -4 z 4 a -4 -4 z 4 -9 a 3 z 3 -18 a z 3 -7 z 3 a -1 + z 3 a -3 - z 3 a -5 -2 a 4 z 2 -3 a 2 z 2 + 2 z 2 a -4 -3 z 2 + 3 a 3 z + 8 a z + 5 z a -1 + 3 a -2 + a -4 + 3-2 a z -1 -3 a -1 z -1 - a -3 z -1$ (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 =

1 is the signature of L11n146. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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