L10n101

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_3,11,4,10 X_7,15,8,14 X_13,5,14,8 X_18,12,19,11 X_20,16,17,15 X_16,20,9,19 X_12,18,13,17 X₂₅₃₆ X_9,1,10,4
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 $u$ , $v$ , $w$ , ...)	$u 3 + v w u 2 - w u 2 + v x u 2 - v w x u 2 - x u 2 - v w u + w u - v x u + x u - u + v w x$ (db)
Jones polynomial	$-q^{17/2}-q^{13/2}-3 q^{11/2}+2 q^{9/2}-4 q^{7/2}+2 q^{5/2}-4 q^{3/2}+2 \sqrt{q}-\frac{1}{\sqrt{q}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$- z 5 a -3 + z 3 a -1 -3 z 3 a -3 + 2 z a -1 - z a -3 -3 z a -5 + 2 z a -7 + a -1 z -1 + a -3 z -1 -6 a -5 z -1 + 5 a -7 z -1 - a -9 z -1 + a -3 z -3 -3 a -5 z -3 + 3 a -7 z -3 - a -9 z -3$ (db)
Kauffman polynomial	$- z 7 a -3 - z 7 a -5 - z 7 a -7 - z 7 a -9 -2 z 6 a -2 -3 z 6 a -4 -2 z 6 a -6 - z 6 a -8 - z 5 a -1 + 4 z 5 a -5 + 10 z 5 a -7 + 7 z 5 a -9 + 5 z 4 a -2 + 10 z 4 a -4 + 14 z 4 a -6 + 9 z 4 a -8 + 3 z 3 a -1 + 6 z 3 a -3 -10 z 3 a -5 -28 z 3 a -7 -15 z 3 a -9 -14 z 2 a -4 -33 z 2 a -6 -19 z 2 a -8 -3 z a -1 + 16 z a -5 + 27 z a -7 + 14 z a -9 - a -2 + 11 a -4 + 24 a -6 + 13 a -8 + a -1 z -1 -3 a -3 z -1 -12 a -5 z -1 -14 a -7 z -1 -6 a -9 z -1 -3 a -4 z -2 -6 a -6 z -2 -3 a -8 z -2 + a -3 z -3 + 3 a -5 z -3 + 3 a -7 z -3 + a -9 z -3$ (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 L10n101. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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