L10a150

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 -2 v w u 3 + w u 3 - u 3 -4 v u 2 + 4 v w u 2 -3 w u 2 + 3 u 2 + 3 v u -3 v w u + 4 w u -4 u - v + v w -2 w + 2$ (db)
Jones polynomial	$q 10 -4 q 9 + 8 q 8 -11 q 7 + 13 q 6 -13 q 5 + 13 q 4 -8 q 3 + 6 q 2 -2 q + 1$ (db)
Signature	4 (db)
HOMFLY-PT polynomial	$- z 6 a -4 - z 6 a -6 + z 4 a -2 -3 z 4 a -4 -2 z 4 a -6 + z 4 a -8 + 3 z 2 a -2 -4 z 2 a -4 + z 2 a -8 + 3 a -2 -4 a -4 + a -6 + a -2 z -2 -2 a -4 z -2 + a -6 z -2$ (db)
Kauffman polynomial	$z 9 a -5 + z 9 a -7 + 2 z 8 a -4 + 7 z 8 a -6 + 5 z 8 a -8 + 2 z 7 a -3 + 6 z 7 a -5 + 13 z 7 a -7 + 9 z 7 a -9 + z 6 a -2 -7 z 6 a -6 + 2 z 6 a -8 + 8 z 6 a -10 -5 z 5 a -3 -18 z 5 a -5 -29 z 5 a -7 -12 z 5 a -9 + 4 z 5 a -11 -4 z 4 a -2 -12 z 4 a -4 -13 z 4 a -6 -15 z 4 a -8 -9 z 4 a -10 + z 4 a -12 + 2 z 3 a -3 + 11 z 3 a -5 + 16 z 3 a -7 + 5 z 3 a -9 -2 z 3 a -11 + 6 z 2 a -2 + 16 z 2 a -4 + 18 z 2 a -6 + 11 z 2 a -8 + 3 z 2 a -10 + 3 z a -3 + z a -5 -3 z a -7 - z a -9 -4 a -2 -8 a -4 -7 a -6 -3 a -8 - a -10 -2 a -3 z -1 -2 a -5 z -1 + a -2 z -2 + 2 a -4 z -2 + a -6 z -2$ (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 =

4 is the signature of L10a150. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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