L10n50

(Knotscape image)

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

Visit L10n50's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_18,9,19,10 X₆₇₁₈ X_13,20,14,7 X_12,5,13,6 X_10,4,11,3 X_4,15,5,16 X_16,12,17,11 X_19,14,20,15 X_2,18,3,17
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 $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + v u 4 + 2 v 2 u 3 -2 v u 3 - v 2 u 2 + v u 2 - u 2 -2 v u + 2 u + v -1$ (db)
Jones polynomial	$q^{3/2}-3 \sqrt{q}+\frac{3}{\sqrt{q}}-\frac{5}{q^{3/2}}+\frac{5}{q^{5/2}}-\frac{5}{q^{7/2}}+\frac{4}{q^{9/2}}-\frac{3}{q^{11/2}}+\frac{1}{q^{13/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- z a 7 + z 5 a 5 + 4 z 3 a 5 + 3 z a 5 - z 7 a 3 -5 z 5 a 3 -7 z 3 a 3 -3 z a 3 + a 3 z -1 + z 5 a + 3 z 3 a - a z -1$ (db)
Kauffman polynomial	$- z 2 a 8 -3 z 3 a 7 + 2 z a 7 - z 6 a 6 -3 z 7 a 5 + 11 z 5 a 5 -15 z 3 a 5 + 6 z a 5 -2 z 8 a 4 + 6 z 6 a 4 -5 z 4 a 4 + 2 z 2 a 4 -6 z 7 a 3 + 23 z 5 a 3 -23 z 3 a 3 + 5 z a 3 + a 3 z -1 -2 z 8 a 2 + 6 z 6 a 2 -2 z 4 a 2 - a 2 -3 z 7 a + 12 z 5 a -11 z 3 a + z a + a z -1 - z 6 + 3 z 4 - z 2$ (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 =

-3 is the signature of L10n50. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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