L10n90

(Knotscape image)

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

Visit L10n90's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$\frac{(t(1)-1) (t(3)-1) \left(t(2) t(3)^2-2 t(2) t(3)+2 t(3)-1\right)}{\sqrt{t(1)} \sqrt{t(2)} t(3)^{3/2}}$ (db)
Jones polynomial	$q 3 -3 q 2 + 5 q -7 + 9 q -1 -7 q -2 + 8 q -3 -5 q -4 + 3 q -5$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$a 6 z -2 + a 6 - z 4 a 4 -3 z 2 a 4 -2 a 4 z -2 -5 a 4 + z 6 a 2 + 4 z 4 a 2 + 7 z 2 a 2 + a 2 z -2 + 6 a 2 -2 z 4 -5 z 2 -3 + z 2 a -2 + a -2$ (db)
Kauffman polynomial	$2 a 2 z 8 + 2 z 8 + 6 a 3 z 7 + 9 a z 7 + 3 z 7 a -1 + 7 a 4 z 6 + 5 a 2 z 6 + z 6 a -2 - z 6 + 3 a 5 z 5 -12 a 3 z 5 -25 a z 5 -10 z 5 a -1 -15 a 4 z 4 -23 a 2 z 4 -3 z 4 a -2 -11 z 4 + 7 a 3 z 3 + 16 a z 3 + 9 z 3 a -1 + 6 a 6 z 2 + 16 a 4 z 2 + 18 a 2 z 2 + 3 z 2 a -2 + 11 z 2 + 3 a 5 z + a 3 z -3 a z - z a -1 -4 a 6 -8 a 4 -7 a 2 - a -2 -3-2 a 5 z -1 -2 a 3 z -1 + a 6 z -2 + 2 a 4 z -2 + a 2 z -2$ (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 =

-2 is the signature of L10n90. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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