L10n73

(Knotscape image)

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

Visit L10n73's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_12,4,13,3 X_7,17,8,16 X_20,9,11,10 X_18,12,19,11 X_15,9,16,8 X_10,19,5,20 X_17,14,18,15 X₂₅₃₆ X_4,14,1,13
Gauss code	{1, -9, 2, -10}, {9, -1, -3, 6, 4, -7}, {5, -2, 10, 8, -6, 3, -8, -5, 7, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 2 - v w u 2 + w u 2 - u 2 + v 2 u -3 v u - v 2 w u + 3 v w u - w u + u - v 2 + v + v 2 w - v w$ (db)
Jones polynomial	$- q 5 + 3 q 4 -4 q 3 + 6 q 2 -6 q + 7-4 q -1 + 4 q -2 - q -3$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$z 4 a -2 + z 4 - a 2 z 2 + z 2 a -2 - z 2 a -4 + a 2 + a -2 -2 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$z 8 a -2 + z 8 + a z 7 + 4 z 7 a -1 + 3 z 7 a -3 + 2 z 6 a -2 + 3 z 6 a -4 - z 6 -8 z 5 a -1 -7 z 5 a -3 + z 5 a -5 + 4 a 2 z 4 -8 z 4 a -2 -8 z 4 a -4 + 4 z 4 + a 3 z 3 + a z 3 + 5 z 3 a -1 + 3 z 3 a -3 -2 z 3 a -5 -3 a 2 z 2 + 5 z 2 a -2 + 4 z 2 a -4 -2 z 2 + 2 a z + 2 z a -1 -2 a 2 -2 a -2 -3-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 =

0 is the signature of L10n73. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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