L11n394

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,7,15,8 X_4,15,1,16 X_9,22,10,19 X₃₈₄₉ X_21,17,22,16 X_11,5,12,18 X_5,21,6,20 X_17,11,18,10 X_19,12,20,13 X_13,2,14,3
Gauss code	{1, 11, -5, -3}, {-10, 8, -6, 4}, {-8, -1, 2, 5, -4, 9, -7, 10, -11, -2, 3, 6, -9, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 5 - v w u 5 -2 v u 4 + 2 v w u 4 + 2 v u 3 -2 v w u 3 + w u 3 - u 3 - v u 2 + v w u 2 -2 w u 2 + 2 u 2 + 2 w u -2 u - w + 1$ (db)
Jones polynomial	$q 3 -3 q 2 + 5 q -6 + 8 q -1 -8 q -2 + 8 q -3 -4 q -4 + 4 q -5 - q -6$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$- a 2 z 8 + a 4 z 6 -6 a 2 z 6 + z 6 + 5 a 4 z 4 -12 a 2 z 4 + 4 z 4 - a 6 z 2 + 7 a 4 z 2 -10 a 2 z 2 + 4 z 2 - a 6 + 2 a 4 -3 a 2 + 2 + a 6 z -2 -2 a 4 z -2 + a 2 z -2$ (db)
Kauffman polynomial	$2 a 3 z 9 + 2 a z 9 + 4 a 4 z 8 + 8 a 2 z 8 + 4 z 8 + 2 a 5 z 7 -4 a 3 z 7 -3 a z 7 + 3 z 7 a -1 -19 a 4 z 6 -35 a 2 z 6 + z 6 a -2 -15 z 6 -6 a 5 z 5 -6 a 3 z 5 -10 a z 5 -10 z 5 a -1 + 4 a 6 z 4 + 37 a 4 z 4 + 51 a 2 z 4 -3 z 4 a -2 + 15 z 4 + a 7 z 3 + 9 a 5 z 3 + 19 a 3 z 3 + 17 a z 3 + 6 z 3 a -1 -6 a 6 z 2 -25 a 4 z 2 -28 a 2 z 2 + z 2 a -2 -8 z 2 - a 7 z - a 5 z -5 a 3 z -7 a z -2 z a -1 - a 6 + 2 a 4 + 5 a 2 + 3-2 a 5 z -1 -2 a 3 z -1 + a 6 z -2 + 2 a 4 z -2 + a 2 z -2$ (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 L11n394. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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