L10a151

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_10,4,11,3 X_14,8,5,7 X_18,14,19,13 X_16,9,17,10 X_8,15,9,16 X_20,17,15,18 X_12,20,13,19 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, -8, 4, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 3 - v w u 3 + w u 3 - u 3 -4 v u 2 + 4 v w u 2 -4 w u 2 + 4 u 2 + 4 v u -4 v w u + 4 w u -4 u - v + v w - w + 1$ (db)
Jones polynomial	$- q 5 + 3 q 4 -6 q 3 + 11 q 2 -12 q + 14-12 q -1 + 11 q -2 -6 q -3 + 3 q -4 - q -5$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 6 + 2 a 2 z 4 + 2 z 4 a -2 -3 z 4 - a 4 z 2 + 4 a 2 z 2 + 4 z 2 a -2 - z 2 a -4 -6 z 2 - a 4 + 4 a 2 + 4 a -2 - a -4 -6 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$a z 9 + z 9 a -1 + 3 a 2 z 8 + 3 z 8 a -2 + 6 z 8 + 4 a 3 z 7 + 9 a z 7 + 9 z 7 a -1 + 4 z 7 a -3 + 3 a 4 z 6 + 4 a 2 z 6 + 4 z 6 a -2 + 3 z 6 a -4 + 2 z 6 + a 5 z 5 -4 a 3 z 5 -15 a z 5 -15 z 5 a -1 -4 z 5 a -3 + z 5 a -5 -6 a 4 z 4 -18 a 2 z 4 -18 z 4 a -2 -6 z 4 a -4 -24 z 4 -2 a 5 z 3 -2 a 3 z 3 + 2 a z 3 + 2 z 3 a -1 -2 z 3 a -3 -2 z 3 a -5 + 5 a 4 z 2 + 18 a 2 z 2 + 18 z 2 a -2 + 5 z 2 a -4 + 26 z 2 + a 5 z + 3 a 3 z + 4 a z + 4 z a -1 + 3 z a -3 + z a -5 -2 a 4 -8 a 2 -8 a -2 -2 a -4 -11-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 L10a151. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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