L10n44

(Knotscape image)

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

Visit L10n44's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_9,19,10,18 X₆₇₁₈ X_13,20,14,7 X_5,13,6,12 X_3,10,4,11 X_15,5,16,4 X_11,16,12,17 X_19,14,20,15 X_17,2,18,3
Gauss code	{1, 10, -6, 7, -5, -3}, {3, -1, -2, 6, -8, 5, -4, 9, -7, 8, -10, 2, -9, 4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 2 + u 2 - v 2 u + 3 v u - u + v 2 - v$ (db)
Jones polynomial	$-\frac{2}{\sqrt{q}}+\frac{2}{q^{3/2}}-\frac{3}{q^{5/2}}+\frac{3}{q^{7/2}}-\frac{3}{q^{9/2}}+\frac{2}{q^{11/2}}-\frac{2}{q^{13/2}}+\frac{1}{q^{15/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z a 7 + z 3 a 5 + z a 5 + z 3 a 3 + z a 3 + a 3 z -1 -2 z a - a z -1$ (db)
Kauffman polynomial	$- z 6 a 8 + 4 z 4 a 8 -3 z 2 a 8 -2 z 7 a 7 + 9 z 5 a 7 -10 z 3 a 7 + 3 z a 7 - z 8 a 6 + 3 z 6 a 6 - z 2 a 6 -3 z 7 a 5 + 13 z 5 a 5 -15 z 3 a 5 + 5 z a 5 - z 8 a 4 + 4 z 6 a 4 -5 z 4 a 4 + 3 z 2 a 4 - z 7 a 3 + 4 z 5 a 3 -5 z 3 a 3 + a 3 z -1 - z 4 a 2 + z 2 a 2 - a 2 -2 z a + a z -1$ (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 =

-1 is the signature of L10n44. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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