L11n334

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_11,16,12,17 X₈₄₉₃ X_2,18,3,17 X_5,14,6,15 X_18,7,19,8 X_15,12,16,5 X_13,20,14,21 X_9,13,10,22 X_21,11,22,10 X_4,19,1,20
Gauss code	{1, -4, 3, -11}, {-5, -1, 6, -3, -9, 10, -2, 7}, {-8, 5, -7, 2, 4, -6, 11, 8, -10, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	0 (db)
Jones polynomial	$q 3 -2 q 2 + 2 q -1 + 2 q -1 + q -2 + 2 q -4 -2 q -5 + 2 q -6 - q -7$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z 2 a 6 - a 6 + z 4 a 4 + 3 z 2 a 4 + a 4 z -2 + 2 a 4 -2 a 2 z -2 - a 2 - z 4 -3 z 2 + z -2 -1 + z 2 a -2 + a -2$ (db)
Kauffman polynomial	$a 5 z 9 + a 3 z 9 + 2 a 6 z 8 + 3 a 4 z 8 + 2 a 2 z 8 + z 8 + a 7 z 7 -4 a 5 z 7 -5 a 3 z 7 + 2 a z 7 + 2 z 7 a -1 -11 a 6 z 6 -20 a 4 z 6 -14 a 2 z 6 + z 6 a -2 -4 z 6 -5 a 7 z 5 -2 a 5 z 5 -12 a z 5 -9 z 5 a -1 + 16 a 6 z 4 + 37 a 4 z 4 + 26 a 2 z 4 -4 z 4 a -2 + z 4 + 6 a 7 z 3 + 12 a 5 z 3 + 13 a 3 z 3 + 15 a z 3 + 8 z 3 a -1 -9 a 6 z 2 -27 a 4 z 2 -20 a 2 z 2 + 3 z 2 a -2 + z 2 -2 a 7 z -7 a 5 z -10 a 3 z -6 a z - z a -1 + 3 a 6 + 9 a 4 + 7 a 2 - a -2 + 1 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 =

-1 is the signature of L11n334. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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