L10a145

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 3 u 3 - v 3 w u 3 + v 2 w u 3 - v 3 u 2 + v 2 u 2 - v 2 w u 2 + v w u 2 - v 2 u + v u - v w u + w u - v - w + 1$ (db)
Jones polynomial	$q 11 -2 q 10 + 3 q 9 -3 q 8 + 4 q 7 -4 q 6 + 4 q 5 -2 q 4 + 3 q 3 - q 2 + q$ (db)
Signature	6 (db)
HOMFLY-PT polynomial	$- z 8 a -6 + z 6 a -4 -7 z 6 a -6 + z 6 a -8 + 6 z 4 a -4 -17 z 4 a -6 + 5 z 4 a -8 + 11 z 2 a -4 -19 z 2 a -6 + 7 z 2 a -8 + 7 a -4 -11 a -6 + 4 a -8 + a -4 z -2 -2 a -6 z -2 + a -8 z -2$ (db)
Kauffman polynomial	$z 9 a -5 + z 9 a -7 + z 8 a -4 + 4 z 8 a -6 + 3 z 8 a -8 -5 z 7 a -5 -2 z 7 a -7 + 3 z 7 a -9 -7 z 6 a -4 -24 z 6 a -6 -14 z 6 a -8 + 3 z 6 a -10 + 4 z 5 a -5 -8 z 5 a -7 -9 z 5 a -9 + 3 z 5 a -11 + 17 z 4 a -4 + 46 z 4 a -6 + 20 z 4 a -8 -6 z 4 a -10 + 3 z 4 a -12 + 9 z 3 a -5 + 19 z 3 a -7 + 4 z 3 a -9 -4 z 3 a -11 + 2 z 3 a -13 -18 z 2 a -4 -35 z 2 a -6 -13 z 2 a -8 -3 z 2 a -12 + z 2 a -14 -11 z a -5 -11 z a -7 + 8 a -4 + 13 a -6 + 5 a -8 + a -12 + 2 a -5 z -1 + 2 a -7 z -1 - a -4 z -2 -2 a -6 z -2 - a -8 z -2$ (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 =

6 is the signature of L10a145. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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