L11n343

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_11,19,12,18 X_7,14,8,15 X_13,8,14,9 X_15,13,16,22 X_17,21,18,20 X_21,17,22,16 X_19,5,20,12 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -10, 2, -11}, {10, -1, -4, 5, 11, -2, -3, 9}, {-5, 4, -6, 8, -7, 3, -9, 7, -8, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 3 + 2 u 3 + 3 v u 2 - v w u 2 + w u 2 -3 u 2 - v u + 3 v w u -3 w u + u -2 v w + 2 w$ (db)
Jones polynomial	$-2 q 3 + 5 q 2 -6 q + 8-8 q -1 + 8 q -2 -5 q -3 + 4 q -4 - q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 6 z -2 + a 6 -2 z 2 a 4 -2 a 4 z -2 -3 a 4 + z 4 a 2 + a 2 z -2 + 2 z 4 + 4 z 2 + 3-2 z 2 a -2 - a -2$ (db)
Kauffman polynomial	$a 3 z 9 + a z 9 + a 4 z 8 + 4 a 2 z 8 + 3 z 8 + a 5 z 7 -2 a 3 z 7 + 3 z 7 a -1 + a 6 z 6 -12 a 2 z 6 + z 6 a -2 -10 z 6 -2 a 5 z 5 + 4 a 3 z 5 -6 z 5 a -1 -5 a 6 z 4 -9 a 4 z 4 + 15 a 2 z 4 + 4 z 4 a -2 + 23 z 4 -3 a 5 z 3 -10 a 3 z 3 - a z 3 + 9 z 3 a -1 + 3 z 3 a -3 + 8 a 6 z 2 + 13 a 4 z 2 -8 a 2 z 2 -7 z 2 a -2 -20 z 2 + 6 a 5 z + 8 a 3 z -4 z a -1 -2 z a -3 -5 a 6 -8 a 4 - a 2 + 2 a -2 + 5-2 a 5 z -1 -2 a 3 z -1 + a 6 z -2 + 2 a 4 z -2 + a 2 z -2$ (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 =

0 is the signature of L11n343. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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