L10n110

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 2 + v x u 2 - v w x u 2 + w x u 2 - x u 2 - v 2 u + 2 v u + v 2 w u -2 v w u + w u + v 2 x u -2 v x u + 2 v w x u - w x u + x u + v 2 - v - v 2 w + v w - v w x$ (db)
Jones polynomial	$-q^{13/2}+3 q^{11/2}-6 q^{9/2}+6 q^{7/2}-10 q^{5/2}+7 q^{3/2}-8 \sqrt{q}+\frac{4}{\sqrt{q}}-\frac{3}{q^{3/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z 5 a -3 -4 z 3 a -1 + 3 z 3 a -3 - z 3 a -5 + 3 a z -9 z a -1 + 7 z a -3 - z a -5 + 3 a z -1 -8 a -1 z -1 + 7 a -3 z -1 -2 a -5 z -1 + a z -3 -3 a -1 z -3 + 3 a -3 z -3 - a -5 z -3$ (db)
Kauffman polynomial	$-2 z 8 a -2 -2 z 8 a -4 -5 z 7 a -1 -9 z 7 a -3 -4 z 7 a -5 - z 6 a -2 - z 6 a -4 -3 z 6 a -6 -3 z 6 + 17 z 5 a -1 + 27 z 5 a -3 + 9 z 5 a -5 - z 5 a -7 + 11 z 4 a -2 + 11 z 4 a -4 + 6 z 4 a -6 + 6 z 4 -6 a z 3 -33 z 3 a -1 -36 z 3 a -3 -7 z 3 a -5 + 2 z 3 a -7 -23 z 2 a -2 -13 z 2 a -4 - z 2 a -6 -11 z 2 + 11 a z + 27 z a -1 + 25 z a -3 + 8 z a -5 - z a -7 + 19 a -2 + 10 a -4 + 10-5 a z -1 -12 a -1 z -1 -12 a -3 z -1 -5 a -5 z -1 -6 a -2 z -2 -3 a -4 z -2 -3 z -2 + a z -3 + 3 a -1 z -3 + 3 a -3 z -3 + a -5 z -3$ (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 =

1 is the signature of L10n110. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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