L10a146

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,4,15,3 X_20,12,13,11 X_18,8,19,7 X_16,10,17,9 X_8,18,9,17 X_10,14,11,13 X_12,20,5,19 X₂₅₃₆ X_4,16,1,15
Gauss code	{1, -9, 2, -10}, {9, -1, 4, -6, 5, -7, 3, -8}, {7, -2, 10, -5, 6, -4, 8, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-\frac{u v^3 w+2 u v^2 w^2-3 u v^2 w+u v^2+u v w^3-3 u v w^2+2 u v w-u w^3+u w^2-v^3 w+v^3-2 v^2 w^2+3 v^2 w-v^2-v w^3+3 v w^2-2 v w-w^2}{\sqrt{u} v^{3/2} w^{3/2}}$ (db)
Jones polynomial	$q 9 -2 q 8 + 5 q 7 -7 q 6 + 10 q 5 -9 q 4 + 10 q 3 -8 q 2 + 5 q -2 + q -1$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$- z 4 a -2 -2 z 4 a -4 - z 4 a -6 -2 z 2 a -4 - z 2 a -6 + z 2 a -8 + z 2 + a -4 -3 a -6 + a -8 + 1 + a -4 z -2 -2 a -6 z -2 + a -8 z -2$ (db)
Kauffman polynomial	$z 9 a -5 + z 9 a -7 + 3 z 8 a -4 + 6 z 8 a -6 + 3 z 8 a -8 + 4 z 7 a -3 + 5 z 7 a -5 + 3 z 7 a -7 + 2 z 7 a -9 + 3 z 6 a -2 -3 z 6 a -4 -18 z 6 a -6 -11 z 6 a -8 + z 6 a -10 + 2 z 5 a -1 -6 z 5 a -3 -17 z 5 a -5 -15 z 5 a -7 -6 z 5 a -9 -2 z 4 a -2 + 3 z 4 a -4 + 28 z 4 a -6 + 18 z 4 a -8 -4 z 4 a -10 + z 4 -2 z 3 a -1 + 6 z 3 a -3 + 21 z 3 a -5 + 17 z 3 a -7 + 4 z 3 a -9 -5 z 2 a -4 -30 z 2 a -6 -19 z 2 a -8 + 4 z 2 a -10 -2 z 2 -11 z a -5 -11 z a -7 + 5 a -4 + 13 a -6 + 8 a -8 + 1 + 2 a -5 z -1 + 2 a -7 z -1 - a -4 z -2 -2 a -6 z -2 - a -8 z -2$ (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 =

2 is the signature of L10a146. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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