L10n93

(Knotscape image)

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

Visit L10n93's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_9,18,10,19 X_17,6,18,1 X_16,7,17,8 X_3,10,4,11 X_5,14,6,15 X_13,4,14,5 X_20,11,13,12 X_12,15,7,16 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 $u$ , $v$ , $w$ , ...)	$- v 2 w 2 u 3 - v w u 2 + v w u + 1$ (db)
Jones polynomial	$q -4 + q -6 + q -9 + q -11$ (db)
Signature	-7 (db)
HOMFLY-PT polynomial	$z 2 a 12 + a 12 z -2 + 2 a 12 - z 6 a 10 -7 z 4 a 10 -14 z 2 a 10 -2 a 10 z -2 -9 a 10 + z 8 a 8 + 8 z 6 a 8 + 21 z 4 a 8 + 21 z 2 a 8 + a 8 z -2 + 7 a 8$ (db)
Kauffman polynomial	$z 2 a 14 -2 a 14 - z 2 a 12 - a 12 z -2 + 3 a 12 + z 7 a 11 -7 z 5 a 11 + 14 z 3 a 11 -9 z a 11 + 2 a 11 z -1 + z 8 a 10 -8 z 6 a 10 + 21 z 4 a 10 -23 z 2 a 10 -2 a 10 z -2 + 11 a 10 + z 7 a 9 -7 z 5 a 9 + 14 z 3 a 9 -9 z a 9 + 2 a 9 z -1 + z 8 a 8 -8 z 6 a 8 + 21 z 4 a 8 -21 z 2 a 8 - a 8 z -2 + 7 a 8$ (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 =

-7 is the signature of L10n93. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -9$	$i = -7$	$i = -5$
$r = -8$		${\mathbb Z}$	${\mathbb Z}$
$r = -7$
$r = -6$		${\mathbb Z}^{2}$	${\mathbb Z}^{2}$
$r = -5$	${\mathbb Z}$	${\mathbb Z}$
$r = -4$		${\mathbb Z}$	${\mathbb Z}$
$r = -3$	${\mathbb Z}$
$r = -2$	${\mathbb Z}_2$	${\mathbb Z}$
$r = -1$
$r = 0$	${\mathbb Z}$	${\mathbb Z}$