L10n102

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_14,7,15,8 X_8,13,5,14 X_11,18,12,19 X_15,20,16,17 X_19,16,20,9 X_17,12,18,13 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -9, 2, -10}, {9, -1, 3, -4}, {-8, 5, -7, 6}, {10, -2, -5, 8, 4, -3, -6, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- w u 3 - x u 3 + u 3 + w u 2 - v w x u 2 + x u 2 + v w u + v x u - u - v w - v x + v w x$ (db)
Jones polynomial	$-\frac{1}{q^{5/2}}+\frac{1}{q^{9/2}}-\frac{3}{q^{11/2}}+\frac{1}{q^{13/2}}-\frac{4}{q^{15/2}}+\frac{2}{q^{17/2}}-\frac{4}{q^{19/2}}+\frac{1}{q^{21/2}}-\frac{1}{q^{23/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$a 13 z -3 -4 a 11 z -1 -3 a 11 z -3 + 5 z a 9 + 7 a 9 z -1 + 3 a 9 z -3 - z 3 a 7 - z a 7 -2 a 7 z -1 - a 7 z -3 - z 5 a 5 -5 z 3 a 5 -4 z a 5 - a 5 z -1$ (db)
Kauffman polynomial	$- z 7 a 13 + 6 z 5 a 13 -13 z 3 a 13 + 13 z a 13 -6 a 13 z -1 + a 13 z -3 - z 8 a 12 + 3 z 6 a 12 + 4 z 4 a 12 -16 z 2 a 12 -3 a 12 z -2 + 13 a 12 -5 z 7 a 11 + 26 z 5 a 11 -41 z 3 a 11 + 31 z a 11 -14 a 11 z -1 + 3 a 11 z -3 - z 8 a 10 + 19 z 4 a 10 -36 z 2 a 10 -6 a 10 z -2 + 24 a 10 -4 z 7 a 9 + 22 z 5 a 9 -36 z 3 a 9 + 26 z a 9 -12 a 9 z -1 + 3 a 9 z -3 -3 z 6 a 8 + 16 z 4 a 8 -21 z 2 a 8 -3 a 8 z -2 + 11 a 8 + z 5 a 7 -3 z 3 a 7 + 4 z a 7 -3 a 7 z -1 + a 7 z -3 + z 4 a 6 - z 2 a 6 - a 6 - z 5 a 5 + 5 z 3 a 5 -4 z a 5 + a 5 z -1$ (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 =

-3 is the signature of L10n102. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -6$	$i = -4$	$i = -2$
$r = -10$		${\mathbb Z}$
$r = -9$		${\mathbb Z}_2$	${\mathbb Z}$
$r = -8$		${\mathbb Z}^{4}$	${\mathbb Z}^{3}$
$r = -7$		${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -6$		${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$		${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -4$	${\mathbb Z}^{3}$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2$	${\mathbb Z}^{2}$
$r = -3$	${\mathbb Z}$	${\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -2$	${\mathbb Z}_2$	${\mathbb Z}$
$r = -1$
$r = 0$	${\mathbb Z}$	${\mathbb Z}$