L10n96

(Knotscape image)

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

Visit L10n96's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X₂₅₃₆ X_13,15,14,20 X_3,11,4,10 X_9,1,10,4 X_7,17,8,16 X_15,5,16,8 X_11,19,12,18 X_19,13,20,12 X_17,9,18,14
Gauss code	{1, -2, -4, 5}, {2, -1, -6, 7}, {-5, 4, -8, 9, -3, 10}, {-7, 6, -10, 8, -9, 3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 2 - v u 2 + v x u 2 - v w x u 2 - v 2 u + 2 v u + v 2 w u - v w u - v x u - v 2 w x u + 2 v w x u - w x u + x u - u - v + v w - v w x + w x$ (db)
Jones polynomial	$- q 19 / 2 + 2 q 17 / 2 -5 q 15 / 2 + 5 q 13 / 2 -8 q 11 / 2 + 6 q 9 / 2 -7 q 7 / 2 + 3 q 5 / 2 -3 q 3 / 2$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$-2 z 5 a -5 + 3 z 3 a -3 -9 z 3 a -5 + 3 z 3 a -7 + 8 z a -3 -16 z a -5 + 9 z a -7 - z a -9 + 5 a -3 z -1 -12 a -5 z -1 + 9 a -7 z -1 -2 a -9 z -1 + a -3 z -3 -3 a -5 z -3 + 3 a -7 z -3 - a -9 z -3$ (db)
Kauffman polynomial	$- z 8 a -6 - z 8 a -8 -4 z 7 a -5 -6 z 7 a -7 -2 z 7 a -9 -3 z 6 a -4 -4 z 6 a -6 -3 z 6 a -8 -2 z 6 a -10 + 15 z 5 a -5 + 18 z 5 a -7 + 2 z 5 a -9 - z 5 a -11 + 9 z 4 a -4 + 18 z 4 a -6 + 13 z 4 a -8 + 4 z 4 a -10 -6 z 3 a -3 -31 z 3 a -5 -26 z 3 a -7 + 2 z 3 a -9 + 3 z 3 a -11 -17 z 2 a -4 -33 z 2 a -6 -16 z 2 a -8 + 13 z a -3 + 28 z a -5 + 21 z a -7 + 3 z a -9 -3 z a -11 + 13 a -4 + 24 a -6 + 11 a -8 - a -10 -6 a -3 z -1 -14 a -5 z -1 -12 a -7 z -1 -3 a -9 z -1 + a -11 z -1 -3 a -4 z -2 -6 a -6 z -2 -3 a -8 z -2 + a -3 z -3 + 3 a -5 z -3 + 3 a -7 z -3 + a -9 z -3$ (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 L10n96. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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