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 $u$ , $v$ , $w$ , ...)	$\frac{-t(1)^3-2 t(2)^2 t(1)^2+2 t(2) t(1)^2+2 t(2)^2 t(1)-2 t(2) t(1)-t(2)^3}{t(1)^{3/2} t(2)^{3/2}}$ (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	$- z 3 a -5 -2 z a -5 - a -5 z -1 + z 5 a -3 + 5 z 3 a -3 + 9 z a -3 + 5 a -3 z -1 - z 5 a -1 + a z 3 -7 z 3 a -1 + 4 a z -13 z a -1 + 4 a z -1 -8 a -1 z -1$ (db)
Kauffman polynomial	$z 5 a -7 -3 z 3 a -7 + z a -7 + 2 z 6 a -6 -7 z 4 a -6 + 5 z 2 a -6 -2 a -6 + z 7 a -5 -2 z 5 a -5 -2 z 3 a -5 + z a -5 + a -5 z -1 + 3 z 6 a -4 -13 z 4 a -4 + 18 z 2 a -4 -9 a -4 + z 7 a -3 -5 z 5 a -3 + 9 z 3 a -3 -8 z a -3 + 5 a -3 z -1 + 2 z 6 a -2 -14 z 4 a -2 + 28 z 2 a -2 -14 a -2 + a z 7 + z 7 a -1 -7 a z 5 -9 z 5 a -1 + 15 a z 3 + 23 z 3 a -1 -13 a z -21 z a -1 + 4 a z -1 + 8 a -1 z -1 + z 6 -8 z 4 + 15 z 2 -8$ (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.

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