L10n94

(Knotscape image)

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

Visit L10n94's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_18,10,19,9 X_6,18,1,17 X_7,17,8,16 X_3,10,4,11 X_14,6,15,5 X_4,14,5,13 X_11,13,12,20 X_15,7,16,12 X_19,3,20,2
Gauss code	{1, 10, -5, -7, 6, -3}, {-4, -1, 2, 5, -8, 9}, {7, -6, -9, 4, 3, -2, -10, 8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$u w v 3 + v 2 - u 2 w 2 v - u w$ (db)
Jones polynomial	$q 9 + q 4 + q 3 + q 2$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$z 4 a -4 - z 4 a -6 + 5 z 2 a -4 -6 z 2 a -6 + z 2 a -8 + 6 a -4 -9 a -6 + 3 a -8 + a -4 z -2 -2 a -6 z -2 + a -8 z -2$ (db)
Kauffman polynomial	$- z 6 a -6 + z 6 a -10 - z 5 a -5 - z 5 a -7 + z 4 a -4 + 7 z 4 a -6 -6 z 4 a -10 + 6 z 3 a -5 + 6 z 3 a -7 -5 z 2 a -4 -15 z 2 a -6 - z 2 a -8 + 9 z 2 a -10 -9 z a -5 -9 z a -7 + 7 a -4 + 11 a -6 + 3 a -8 -2 a -10 + 2 a -5 z -1 + 2 a -7 z -1 - a -4 z -2 -2 a -6 z -2 - a -8 z -2$ (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 L10n94. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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