L11n184

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_9,21,10,20 X_6,21,1,22 X_18,8,19,7 X_3,10,4,11 X_15,12,16,13 X_5,14,6,15 X_13,4,14,5 X_11,16,12,17 X_22,18,7,17 X_19,2,20,3
Gauss code	{1, 11, -5, 8, -7, -3}, {4, -1, -2, 5, -9, 6, -8, 7, -6, 9, 10, -4, -11, 2, 3, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 4 + u 4 + 2 v u 3 -2 u 3 - v u 2 -2 v 2 u + 2 v u + v 2 -2 v$ (db)
Jones polynomial	$\sqrt{q}-\frac{2}{\sqrt{q}}+\frac{3}{q^{3/2}}-\frac{5}{q^{5/2}}+\frac{4}{q^{7/2}}-\frac{5}{q^{9/2}}+\frac{4}{q^{11/2}}-\frac{3}{q^{13/2}}+\frac{2}{q^{15/2}}-\frac{1}{q^{17/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z 3 a 7 + 2 z a 7 - z 5 a 5 -3 z 3 a 5 - z a 5 + 2 a 5 z -1 - z 5 a 3 -4 z 3 a 3 -6 z a 3 -3 a 3 z -1 + z 3 a + 2 z a + a z -1$ (db)
Kauffman polynomial	$- z 7 a 9 + 5 z 5 a 9 -7 z 3 a 9 + 3 z a 9 -2 z 8 a 8 + 10 z 6 a 8 -14 z 4 a 8 + 6 z 2 a 8 - z 9 a 7 + 2 z 7 a 7 + 6 z 5 a 7 -10 z 3 a 7 + 2 z a 7 -4 z 8 a 6 + 18 z 6 a 6 -22 z 4 a 6 + 9 z 2 a 6 - z 9 a 5 + z 7 a 5 + 9 z 5 a 5 -14 z 3 a 5 + 7 z a 5 -2 a 5 z -1 -2 z 8 a 4 + 7 z 6 a 4 -5 z 4 a 4 -2 z 2 a 4 + 3 a 4 -2 z 7 a 3 + 8 z 5 a 3 -13 z 3 a 3 + 10 z a 3 -3 a 3 z -1 - z 6 a 2 + 3 z 4 a 2 -6 z 2 a 2 + 3 a 2 -2 z 3 a + 2 z a - a z -1 - z 2 + 1$ (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 =

-1 is the signature of L11n184. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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