L10a155

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 - v w u 3 -2 u 3 -6 v u 2 + 4 v w u 2 -4 w u 2 + 5 u 2 + 4 v u -5 v w u + 6 w u -4 u + 2 v w -2 w + 1$ (db)
Jones polynomial	$q 4 -4 q 3 + 10 q 2 -12 q + 16-16 q -1 + 15 q -2 -11 q -3 + 7 q -4 -3 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 6 -3 z 2 a 4 -2 a 4 + 3 z 4 a 2 + 5 z 2 a 2 + a 2 z -2 + 4 a 2 - z 6 -3 z 4 -7 z 2 -2 z -2 -6 + z 4 a -2 + z 2 a -2 + a -2 z -2 + 3 a -2$ (db)
Kauffman polynomial	$2 a 3 z 9 + 2 a z 9 + 4 a 4 z 8 + 12 a 2 z 8 + 8 z 8 + 3 a 5 z 7 + 7 a 3 z 7 + 16 a z 7 + 12 z 7 a -1 + a 6 z 6 -7 a 4 z 6 -21 a 2 z 6 + 10 z 6 a -2 -3 z 6 -8 a 5 z 5 -27 a 3 z 5 -38 a z 5 -15 z 5 a -1 + 4 z 5 a -3 -3 a 6 z 4 + 4 a 2 z 4 -12 z 4 a -2 + z 4 a -4 -12 z 4 + 7 a 5 z 3 + 23 a 3 z 3 + 17 a z 3 + z 3 a -1 + 3 a 6 z 2 + 4 a 4 z 2 + 3 a 2 z 2 + 8 z 2 a -2 + 10 z 2 -2 a 5 z -6 a 3 z + 2 a z + 6 z a -1 - a 6 -2 a 2 -5 a -2 -7-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 =

0 is the signature of L10a155. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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