L11n395

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,7,15,8 X_15,1,16,4 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_2,14,3,13
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 $u$ , $v$ , $w$ , ...)	$v u 3 - v w u 3 + w u 3 - u 3 -2 v u 2 + 2 v w u 2 -2 w u 2 + 2 u 2 + 2 v u -2 v w u + 2 w u -2 u - v + v w - w + 1$ (db)
Jones polynomial	$q 5 -4 q 4 + 6 q 3 -6 q 2 + 9 q -7 + 7 q -1 -4 q -2 + 3 q -3 - q -4$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$z 6 - a 2 z 4 -2 z 4 a -2 + 4 z 4 -2 a 2 z 2 -4 z 2 a -2 + z 2 a -4 + 5 z 2 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$2 a z 9 + 2 z 9 a -1 + 3 a 2 z 8 + 5 z 8 a -2 + 8 z 8 + a 3 z 7 -5 a z 7 - z 7 a -1 + 5 z 7 a -3 -14 a 2 z 6 -18 z 6 a -2 + 2 z 6 a -4 -34 z 6 -4 a 3 z 5 -5 a z 5 -17 z 5 a -1 -16 z 5 a -3 + 19 a 2 z 4 + 22 z 4 a -2 - z 4 a -4 + 42 z 4 + 4 a 3 z 3 + 13 a z 3 + 22 z 3 a -1 + 17 z 3 a -3 + 4 z 3 a -5 -8 a 2 z 2 -13 z 2 a -2 - z 2 a -4 + z 2 a -6 -19 z 2 - a 3 z -4 a z -6 z a -1 -4 z a -3 - z a -5 + 1-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 =

2 is the signature of L11n395. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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