L10n24

(Knotscape image)

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

Visit L10n24's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_10,4,11,3 X_12,8,13,7 X_13,18,14,19 X_9,17,10,16 X_17,9,18,8 X_15,20,16,5 X_19,14,20,15 X₂₅₃₆ X_4,12,1,11
Gauss code	{1, -9, 2, -10}, {9, -1, 3, 6, -5, -2, 10, -3, -4, 8, -7, 5, -6, 4, -8, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 3 + u 3 + v u 2 - u 2 - v u + u + v -1$ (db)
Jones polynomial	$q^{9/2}-2 q^{7/2}+2 q^{5/2}-3 q^{3/2}+2 \sqrt{q}-\frac{3}{\sqrt{q}}+\frac{2}{q^{3/2}}-\frac{1}{q^{5/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z 5 a -1 + a z 3 -4 z 3 a -1 + z 3 a -3 + 2 a z -4 z a -1 + 2 z a -3 + a z -1 - a -1 z -1$ (db)
Kauffman polynomial	$- z 8 a -2 - z 8 - a z 7 -3 z 7 a -1 -2 z 7 a -3 + 3 z 6 a -2 - z 6 a -4 + 4 z 6 + 5 a z 5 + 14 z 5 a -1 + 9 z 5 a -3 + z 4 a -2 + 4 z 4 a -4 -3 z 4 -8 a z 3 -18 z 3 a -1 -10 z 3 a -3 - a 2 z 2 -3 z 2 a -2 -3 z 2 a -4 - z 2 + 4 a z + 8 z a -1 + 4 z a -3 + 1- a z -1 - a -1 z -1$ (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 L10n24. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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