L10n104

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_5,12,6,13 X₃₈₄₉ X_15,2,16,3 X_7,17,8,16 X_14,9,11,10 X_20,13,15,14 X_19,5,20,10 X_11,18,12,19 X_4,17,1,18
Gauss code	{1, 4, -3, -10}, {-9, 2, 7, -6}, {-2, -1, -5, 3, 6, 8}, {-4, 5, 10, 9, -8, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 w 2 - v w - u v x w + u x$ (db)
Jones polynomial	$-\frac{1}{q^{3/2}}-\frac{1}{q^{5/2}}-\frac{2}{q^{7/2}}-\frac{1}{q^{9/2}}-\frac{1}{q^{11/2}}-\frac{1}{q^{13/2}}-\frac{1}{q^{17/2}}$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$a 9 z -1 + a 9 z -3 -2 z a 7 -6 a 7 z -1 -3 a 7 z -3 + z 3 a 5 + 6 z a 5 + 9 a 5 z -1 + 3 a 5 z -3 - z 3 a 3 -4 z a 3 -4 a 3 z -1 - a 3 z -3$ (db)
Kauffman polynomial	$- z 7 a 9 + 7 z 5 a 9 -15 z 3 a 9 + 12 z a 9 -5 a 9 z -1 + a 9 z -3 - z 6 a 8 + 7 z 4 a 8 -14 z 2 a 8 -3 a 8 z -2 + 10 a 8 - z 7 a 7 + 8 z 5 a 7 -21 z 3 a 7 + 23 z a 7 -12 a 7 z -1 + 3 a 7 z -3 - z 6 a 6 + 8 z 4 a 6 -20 z 2 a 6 -6 a 6 z -2 + 19 a 6 + z 5 a 5 -7 z 3 a 5 + 15 z a 5 -12 a 5 z -1 + 3 a 5 z -3 + z 4 a 4 -6 z 2 a 4 -3 a 4 z -2 + 10 a 4 - z 3 a 3 + 4 z a 3 -5 a 3 z -1 + a 3 z -3$ (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 =

-2 is the signature of L10n104. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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