L8a16

(Knotscape image)

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

Visit L8a16's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_12,6,13,5 X₈₄₉₃ X_2,14,3,13 X_14,7,15,8 X_16,10,11,9 X_10,12,5,11 X_4,15,1,16
Gauss code	{1, -4, 3, -8}, {2, -1, 5, -3, 6, -7}, {7, -2, 4, -5, 8, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 2 - v u 2 - v 2 w u 2 + v w u 2 - v 2 u + 2 v u + v 2 w u -2 v w u + w u - u - v + v w - w + 1$ (db)
Jones polynomial	$- q 6 + 3 q 5 -4 q 4 + 6 q 3 -5 q 2 + 6 q -3 + 3 q -1 - q -2$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$z 6 a -2 + 4 z 4 a -2 - z 4 a -4 - z 4 + 4 z 2 a -2 -2 z 2 a -4 -2 z 2 - a -2 + 1-2 a -2 z -2 + a -4 z -2 + z -2$ (db)
Kauffman polynomial	$2 z 7 a -1 + 2 z 7 a -3 + 7 z 6 a -2 + 4 z 6 a -4 + 3 z 6 + a z 5 -3 z 5 a -1 + 4 z 5 a -5 -17 z 4 a -2 -5 z 4 a -4 + 3 z 4 a -6 -9 z 4 -2 a z 3 - z 3 a -1 -3 z 3 a -3 -3 z 3 a -5 + z 3 a -7 + 10 z 2 a -2 + 2 z 2 a -4 -2 z 2 a -6 + 6 z 2 - z a -1 - z a -3 + a -2 + a -4 + 1 + 2 a -1 z -1 + 2 a -3 z -1 -2 a -2 z -2 - a -4 z -2 - z -2$ (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 =

2 is the signature of L8a16. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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