L10n46

(Knotscape image)

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

Visit L10n46's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_9,19,10,18 X₆₇₁₈ X_13,20,14,7 X_12,5,13,6 X_3,10,4,11 X_4,15,5,16 X_16,12,17,11 X_19,14,20,15 X_17,2,18,3
Gauss code	{1, 10, -6, -7, 5, -3}, {3, -1, -2, 6, 8, -5, -4, 9, 7, -8, -10, 2, -9, 4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 4 -2 v u 3 - v 2 u 2 + v u 2 - u 2 -2 v u + v$ (db)
Jones polynomial	$-\frac{2}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{4}{q^{9/2}}-\frac{3}{q^{11/2}}+\frac{2}{q^{13/2}}-\frac{2}{q^{15/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$a 9 z -1 - z 3 a 7 -3 z a 7 -2 a 7 z -1 + z 5 a 5 + 4 z 3 a 5 + 5 z a 5 + 2 a 5 z -1 -2 z 3 a 3 -5 z a 3 - a 3 z -1$ (db)
Kauffman polynomial	$-3 z 3 a 9 + 6 z a 9 - a 9 z -1 - z 6 a 8 + 2 z 4 a 8 -2 z 2 a 8 - z 7 a 7 + 4 z 5 a 7 -11 z 3 a 7 + 10 z a 7 -2 a 7 z -1 -2 z 6 a 6 + 4 z 4 a 6 -4 z 2 a 6 - a 6 - z 7 a 5 + 4 z 5 a 5 -11 z 3 a 5 + 10 z a 5 -2 a 5 z -1 - z 6 a 4 + 2 z 4 a 4 -2 z 2 a 4 -3 z 3 a 3 + 6 z a 3 - a 3 z -1$ (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 L10n46. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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