L11n376

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,7,15,8 X_4,15,1,16 X_5,10,6,11 X₃₈₄₉ X_22,18,19,17 X_11,20,12,21 X_19,12,20,13 X_18,22,5,21 X_9,16,10,17 X_13,2,14,3
Gauss code	{1, 11, -5, -3}, {-8, 7, 9, -6}, {-4, -1, 2, 5, -10, 4, -7, 8, -11, -2, 3, 10, 6, -9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 3 - v w u 3 - v u 2 + v w u 2 + w u - u - w + 1$ (db)
Jones polynomial	$2 q -2 - q -3 + 3 q -4 -2 q -5 + 4 q -6 -2 q -7 + q -8 - q -9$ (db)
Signature	-4 (db)
HOMFLY-PT polynomial	$- a 10 z -2 - a 10 + z 4 a 8 + 5 z 2 a 8 + 4 a 8 z -2 + 7 a 8 - z 6 a 6 -6 z 4 a 6 -13 z 2 a 6 -5 a 6 z -2 -13 a 6 + 2 z 4 a 4 + 8 z 2 a 4 + 2 a 4 z -2 + 7 a 4$ (db)
Kauffman polynomial	$z 3 a 11 -3 z a 11 + a 11 z -1 + z 4 a 10 -2 z 2 a 10 - a 10 z -2 + 2 a 10 + z 7 a 9 -6 z 5 a 9 + 15 z 3 a 9 -14 z a 9 + 5 a 9 z -1 + z 8 a 8 -6 z 6 a 8 + 14 z 4 a 8 -13 z 2 a 8 -4 a 8 z -2 + 11 a 8 + 2 z 7 a 7 -11 z 5 a 7 + 25 z 3 a 7 -24 z a 7 + 9 a 7 z -1 + z 8 a 6 -6 z 6 a 6 + 16 z 4 a 6 -22 z 2 a 6 -5 a 6 z -2 + 16 a 6 + z 7 a 5 -5 z 5 a 5 + 11 z 3 a 5 -13 z a 5 + 5 a 5 z -1 + 3 z 4 a 4 -11 z 2 a 4 -2 a 4 z -2 + 8 a 4$ (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 =

-4 is the signature of L11n376. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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