L10n92

(Knotscape image)

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

Visit L10n92's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_18,10,19,9 X_17,6,18,1 X_7,17,8,16 X_3,10,4,11 X_5,14,6,15 X_13,4,14,5 X_11,13,12,20 X_15,7,16,12 X_2,19,3,20
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 $u$ , $v$ , $w$ , ...)	$v 2 w u 3 + v 2 u 2 - v 2 w u 2 + v w u 2 - w 2 u - v w u + w u - w$ (db)
Jones polynomial	$q 2 - q + 3-2 q -1 + 3 q -2 -2 q -3 + 2 q -4 - q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- a 2 z 6 + a 4 z 4 -6 a 2 z 4 + z 4 + 4 a 4 z 2 -12 a 2 z 2 + 4 z 2 + 4 a 4 -9 a 2 + 5 + a 4 z -2 -2 a 2 z -2 + z -2$ (db)
Kauffman polynomial	$a 4 z 8 + a 2 z 8 + a 5 z 7 + 2 a 3 z 7 + a z 7 + a 6 z 6 -5 a 4 z 6 -6 a 2 z 6 -4 a 5 z 5 -9 a 3 z 5 -5 a z 5 -5 a 6 z 4 + 9 a 4 z 4 + 16 a 2 z 4 + 2 z 4 + 3 a 5 z 3 + 13 a 3 z 3 + 11 a z 3 + z 3 a -1 + 6 a 6 z 2 -10 a 4 z 2 -21 a 2 z 2 + z 2 a -2 -4 z 2 -9 a 3 z -9 a z - a 6 + 5 a 4 + 11 a 2 - a -2 + 5 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 =

0 is the signature of L10n92. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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