L11n226

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_18,11,19,12 X_6,9,7,10 X_7,21,8,20 X_19,1,20,8 X_22,15,9,16 X_3,12,4,13 X_16,6,17,5 X_13,4,14,5 X_14,21,15,22 X_2,18,3,17
Gauss code	{1, -11, -7, 9, 8, -3, -4, 5}, {3, -1, 2, 7, -9, -10, 6, -8, 11, -2, -5, 4, 10, -6}

A Braid Representative

A Morse Link Presentation

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

-2 is the signature of L11n226. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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