L11a94

(Knotscape image)

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

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Planar diagram presentation	X₆₁₇₂ X_12,4,13,3 X_20,8,21,7 X_22,17,5,18 X_18,21,19,22 X_16,10,17,9 X_14,12,15,11 X_10,16,11,15 X_8,20,9,19 X₂₅₃₆ X_4,14,1,13
Gauss code	{1, -10, 2, -11}, {10, -1, 3, -9, 6, -8, 7, -2, 11, -7, 8, -6, 4, -5, 9, -3, 5, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 3 + 2 u 3 + 9 v u 2 -9 u 2 -9 v u + 9 u + 2 v -2$ (db)
Jones polynomial	$q^{15/2}-3 q^{13/2}+6 q^{11/2}-10 q^{9/2}+12 q^{7/2}-14 q^{5/2}+14 q^{3/2}-12 \sqrt{q}+\frac{8}{\sqrt{q}}-\frac{5}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{1}{q^{7/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z 5 a -1 + z 5 a -3 -2 a z 3 + z 3 a -1 -2 z 3 a -5 + a 3 z -3 a z + 3 z a -1 - z a -3 - z a -5 + z a -7 + a 3 z -1 -2 a z -1 + 2 a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$- z 10 a -2 - z 10 a -4 -2 z 9 a -1 -5 z 9 a -3 -3 z 9 a -5 -2 z 8 a -2 -4 z 8 a -4 -4 z 8 a -6 -2 z 8 -2 a z 7 + z 7 a -1 + 10 z 7 a -3 + 4 z 7 a -5 -3 z 7 a -7 -2 a 2 z 6 + 2 z 6 a -2 + 13 z 6 a -4 + 10 z 6 a -6 - z 6 a -8 -2 z 6 - a 3 z 5 - a z 5 -5 z 5 a -1 -10 z 5 a -3 + 4 z 5 a -5 + 9 z 5 a -7 + 4 a 2 z 4 + z 4 a -2 -10 z 4 a -4 -5 z 4 a -6 + 3 z 4 a -8 + 7 z 4 + 3 a 3 z 3 + 9 a z 3 + 10 z 3 a -1 + 6 z 3 a -3 -5 z 3 a -5 -7 z 3 a -7 -2 a 2 z 2 -3 z 2 a -2 + 2 z 2 a -4 + z 2 a -6 -2 z 2 a -8 -4 z 2 -3 a 3 z -8 a z -8 z a -1 -3 z a -3 + 2 z a -5 + 2 z a -7 + 1 + a 3 z -1 + 2 a z -1 + 2 a -1 z -1 + a -3 z -1$ (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 =

1 is the signature of L11a94. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 0$	$i = 2$
$r = -4$	${\mathbb Z}$
$r = -3$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -1$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 0$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{6}$
$r = 1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 2$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 4$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 5$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 6$	${\mathbb Z}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 7$	${\mathbb Z}_2$	${\mathbb Z}$