L10n60

(Knotscape image)

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

Visit L10n60's page at the original Knot Atlas.

Planar diagram presentation	X_12,1,13,2 X_16,7,17,8 X_5,1,6,10 X₃₇₄₆ X_9,5,10,4 X_17,11,18,20 X_13,19,14,18 X_19,15,20,14 X_2,11,3,12 X_8,15,9,16
Gauss code	{1, -9, -4, 5, -3, 4, 2, -10, -5, 3}, {9, -1, -7, 8, 10, -2, -6, 7, -8, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- u 3 -2 v 2 u 2 + 2 v u 2 + 2 v 2 u -2 v u - v 3$ (db)
Jones polynomial	$-q^{13/2}+2 q^{11/2}-2 q^{9/2}+3 q^{7/2}-2 q^{5/2}+2 q^{3/2}-2 \sqrt{q}-\frac{1}{\sqrt{q}}-\frac{1}{q^{5/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 5 a -1 + z 5 a -3 + a z 3 -7 z 3 a -1 + 5 z 3 a -3 - z 3 a -5 + 4 a z -13 z a -1 + 9 z a -3 -2 z a -5 + 4 a z -1 -8 a -1 z -1 + 5 a -3 z -1 - a -5 z -1$ (db)
Kauffman polynomial	$- a z 7 - z 7 a -1 - z 7 a -3 - z 7 a -5 -2 z 6 a -2 -3 z 6 a -4 -2 z 6 a -6 - z 6 + 7 a z 5 + 9 z 5 a -1 + 5 z 5 a -3 + 2 z 5 a -5 - z 5 a -7 + 14 z 4 a -2 + 13 z 4 a -4 + 7 z 4 a -6 + 8 z 4 -15 a z 3 -23 z 3 a -1 -9 z 3 a -3 + 2 z 3 a -5 + 3 z 3 a -7 -28 z 2 a -2 -18 z 2 a -4 -5 z 2 a -6 -15 z 2 + 13 a z + 21 z a -1 + 8 z a -3 - z a -5 - z a -7 + 14 a -2 + 9 a -4 + 2 a -6 + 8-4 a z -1 -8 a -1 z -1 -5 a -3 z -1 - a -5 z -1$ (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 L10n60. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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