L10a43

(Knotscape image)

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

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Planar diagram presentation	X₆₁₇₂ X_2,9,3,10 X_12,3,13,4 X_20,12,5,11 X_18,6,19,5 X_10,20,11,19 X_4,17,1,18 X_16,14,17,13 X_14,8,15,7 X_8,16,9,15
Gauss code	{1, -2, 3, -7}, {5, -1, 9, -10, 2, -6, 4, -3, 8, -9, 10, -8, 7, -5, 6, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 + 4 v u 4 -4 u 4 -8 v u 3 + 8 u 3 + 8 v u 2 -8 u 2 -4 v u + 4 u -1$ (db)
Jones polynomial	$-q^{13/2}+5 q^{11/2}-9 q^{9/2}+13 q^{7/2}-16 q^{5/2}+17 q^{3/2}-16 \sqrt{q}+\frac{11}{\sqrt{q}}-\frac{8}{q^{3/2}}+\frac{3}{q^{5/2}}-\frac{1}{q^{7/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -1 + a z 5 -5 z 5 a -1 + 2 z 5 a -3 + 3 a z 3 -12 z 3 a -1 + 5 z 3 a -3 - z 3 a -5 + 5 a z -12 z a -1 + 5 z a -3 + 3 a z -1 -5 a -1 z -1 + 2 a -3 z -1$ (db)
Kauffman polynomial	$-2 z 9 a -1 -2 z 9 a -3 -12 z 8 a -2 -7 z 8 a -4 -5 z 8 -6 a z 7 -12 z 7 a -1 -15 z 7 a -3 -9 z 7 a -5 -3 a 2 z 6 + 13 z 6 a -2 + 4 z 6 a -4 -5 z 6 a -6 + z 6 - a 3 z 5 + 12 a z 5 + 31 z 5 a -1 + 34 z 5 a -3 + 15 z 5 a -5 - z 5 a -7 + 4 a 2 z 4 + 10 z 4 a -2 + 9 z 4 a -4 + 6 z 4 a -6 + 11 z 4 + 2 a 3 z 3 -14 a z 3 -29 z 3 a -1 -18 z 3 a -3 -5 z 3 a -5 - a 2 z 2 -17 z 2 a -2 -4 z 2 a -4 -14 z 2 - a 3 z + 10 a z + 16 z a -1 + 5 z a -3 + 5 a -2 - a -6 + 5-3 a z -1 -5 a -1 z -1 -2 a -3 z -1$ (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 L10a43. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 0$	$i = 2$
$r = -4$	${\mathbb Z}$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{3}$
$r = -2$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -1$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 0$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{7}$
$r = 1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 2$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 3$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 4$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 5$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 6$	${\mathbb Z}_2$	${\mathbb Z}$