L11n247

(Knotscape image)

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

Planar diagram presentation	X_12,1,13,2 X₃₈₄₉ X_14,6,15,5 X_7,18,8,19 X_9,21,10,20 X_10,11,1,12 X_6,14,7,13 X_17,4,18,5 X_15,11,16,22 X_19,3,20,2 X_21,17,22,16
Gauss code	{1, 10, -2, 8, 3, -7, -4, 2, -5, -6}, {6, -1, 7, -3, -9, 11, -8, 4, -10, 5, -11, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	0 (db)
Jones polynomial	$q^{9/2}-2 q^{7/2}+q^{5/2}-q^{3/2}-\frac{1}{q^{3/2}}+\frac{1}{q^{5/2}}-\frac{2}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a z 5 - z 5 a -1 - a 3 z 3 + 5 a z 3 -5 z 3 a -1 + z 3 a -3 -2 a 3 z + 6 a z -6 z a -1 + 2 z a -3 + a z -1 - a -1 z -1$ (db)
Kauffman polynomial	$- a 2 z 8 - z 8 a -2 -2 z 8 -2 a 3 z 7 -3 a z 7 -3 z 7 a -1 -2 z 7 a -3 - a 4 z 6 + 5 a 2 z 6 + 5 z 6 a -2 - z 6 a -4 + 12 z 6 + 10 a 3 z 5 + 19 a z 5 + 19 z 5 a -1 + 10 z 5 a -3 + 4 a 4 z 4 -4 a 2 z 4 -4 z 4 a -2 + 4 z 4 a -4 -16 z 4 -11 a 3 z 3 -29 a z 3 -29 z 3 a -1 -11 z 3 a -3 -2 a 4 z 2 -2 z 2 a -4 + 4 z 2 + 4 a 3 z + 12 a z + 12 z a -1 + 4 z a -3 + 1- a z -1 - a -1 z -1$ (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 =

0 is the signature of L11n247. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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