L11n283

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,6,13,5 X₈₄₉₃ X_2,14,3,13 X_14,7,15,8 X_9,18,10,19 X_17,11,18,22 X_11,21,12,20 X_21,17,22,16 X_4,15,1,16 X_19,10,20,5
Gauss code	{1, -4, 3, -10}, {2, -1, 5, -3, -6, 11}, {-8, -2, 4, -5, 10, 9, -7, 6, -11, 8, -9, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 2 -2 v u 2 - v 2 w u 2 + 2 v w u 2 - w u 2 + u 2 -2 v 2 u + 4 v u + 2 v 2 w u -4 v w u + 2 w u -2 u + v 2 -2 v - v 2 w + 2 v w - w + 1$ (db)
Jones polynomial	$q 6 -4 q 5 + 6 q 4 -9 q 3 + 11 q 2 -10 q + 11-6 q -1 + 5 q -2 - q -3$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 6 a -2 -3 z 4 a -2 + z 4 a -4 + 2 z 4 - a 2 z 2 -2 z 2 a -2 + z 2 a -4 + 2 z 2 + a 2 + 4 a -2 - a -4 -4 + 2 a 2 z -2 + 4 a -2 z -2 - a -4 z -2 -5 z -2$ (db)
Kauffman polynomial	$2 z 9 a -1 + 2 z 9 a -3 + 9 z 8 a -2 + 5 z 8 a -4 + 4 z 8 + 2 a z 7 + 2 z 7 a -3 + 4 z 7 a -5 -28 z 6 a -2 -15 z 6 a -4 + z 6 a -6 -12 z 6 - a z 5 -8 z 5 a -1 -19 z 5 a -3 -12 z 5 a -5 + 5 a 2 z 4 + 29 z 4 a -2 + 11 z 4 a -4 -2 z 4 a -6 + 21 z 4 + a 3 z 3 + a z 3 + 6 z 3 a -1 + 13 z 3 a -3 + 7 z 3 a -5 -3 a 2 z 2 -12 z 2 a -2 -4 z 2 a -4 -11 z 2 + 5 a z + 9 z a -1 + 5 z a -3 + z a -5 -3 a 2 -2 a -2 -4-5 a z -1 -9 a -1 z -1 -5 a -3 z -1 - a -5 z -1 + 2 a 2 z -2 + 4 a -2 z -2 + a -4 z -2 + 5 z -2$ (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 =

0 is the signature of L11n283. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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