L11n294

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,4,13,3 X_20,16,21,15 X_14,8,15,7 X_10,22,5,21 X_11,19,12,18 X_9,17,10,16 X_17,11,18,22 X_19,9,20,8 X₂₅₃₆ X_4,14,1,13
Gauss code	{1, -10, 2, -11}, {10, -1, 4, 9, -7, -5}, {-6, -2, 11, -4, 3, 7, -8, 6, -9, -3, 5, 8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 4 - v 2 w u 4 + v w u 4 - v 2 u 3 + v u 2 - v w u 2 + w u - v - w + 1$ (db)
Jones polynomial	$- q 8 + q 7 - q 6 + 3 q 5 - q 4 + 3 q 3 - q 2 + q$ (db)
Signature	6 (db)
HOMFLY-PT polynomial	$- z 8 a -6 + z 6 a -4 -7 z 6 a -6 + z 6 a -8 + 6 z 4 a -4 -17 z 4 a -6 + 6 z 4 a -8 + 11 z 2 a -4 -21 z 2 a -6 + 10 z 2 a -8 - z 2 a -10 + 8 a -4 -15 a -6 + 8 a -8 - a -10 + 2 a -4 z -2 -5 a -6 z -2 + 4 a -8 z -2 - a -10 z -2$ (db)
Kauffman polynomial	$z 9 a -5 + z 9 a -7 + z 8 a -4 + 4 z 8 a -6 + 3 z 8 a -8 -5 z 7 a -5 -3 z 7 a -7 + 2 z 7 a -9 -7 z 6 a -4 -26 z 6 a -6 -19 z 6 a -8 + 3 z 5 a -5 -9 z 5 a -7 -12 z 5 a -9 + 17 z 4 a -4 + 53 z 4 a -6 + 36 z 4 a -8 + 12 z 3 a -5 + 31 z 3 a -7 + 19 z 3 a -9 -19 z 2 a -4 -45 z 2 a -6 -29 z 2 a -8 -3 z 2 a -10 -16 z a -5 -27 z a -7 -13 z a -9 -2 z a -11 + 10 a -4 + 20 a -6 + 13 a -8 + 2 a -10 + 5 a -5 z -1 + 9 a -7 z -1 + 5 a -9 z -1 + a -11 z -1 -2 a -4 z -2 -5 a -6 z -2 -4 a -8 z -2 - a -10 z -2$ (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 =

6 is the signature of L11n294. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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