L9n1

(Knotscape image)

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

Visit L9n1's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_14,7,15,8 X_4,15,1,16 X_5,10,6,11 X₃₈₄₉ X_11,18,12,5 X_17,12,18,13 X_9,16,10,17 X_13,2,14,3
Gauss code	{1, 9, -5, -3}, {-4, -1, 2, 5, -8, 4, -6, 7, -9, -2, 3, 8, -7, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 3 + v u 2 + u -2$ (db)
Jones polynomial	$-\frac{1}{q^{5/2}}+\frac{1}{q^{7/2}}-\frac{2}{q^{9/2}}+\frac{1}{q^{11/2}}-\frac{3}{q^{13/2}}+\frac{2}{q^{15/2}}-\frac{1}{q^{17/2}}+\frac{1}{q^{19/2}}$ (db)
Signature	-5 (db)
HOMFLY-PT polynomial	$- a 11 z -1 + z 3 a 9 + 4 z a 9 + 2 a 9 z -1 - z 5 a 7 -4 z 3 a 7 -3 z a 7 - z 5 a 5 -4 z 3 a 5 -3 z a 5 - a 5 z -1$ (db)
Kauffman polynomial	$- z 2 a 12 + 2 a 12 - z 3 a 11 + z a 11 - a 11 z -1 - z 6 a 10 + 5 z 4 a 10 -10 z 2 a 10 + 5 a 10 - z 7 a 9 + 5 z 5 a 9 -9 z 3 a 9 + 5 z a 9 -2 a 9 z -1 -2 z 6 a 8 + 8 z 4 a 8 -9 z 2 a 8 + 3 a 8 - z 7 a 7 + 4 z 5 a 7 -4 z 3 a 7 + z a 7 - z 6 a 6 + 3 z 4 a 6 - a 6 - z 5 a 5 + 4 z 3 a 5 -3 z a 5 + a 5 z -1$ (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 =

-5 is the signature of L9n1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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