L10n71

(Knotscape image)

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

Visit L10n71's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_3,12,4,13 X_7,17,8,16 X_9,11,10,20 X_11,18,12,19 X_15,9,16,8 X_19,5,20,10 X_17,14,18,15 X₂₅₃₆ X_13,4,14,1
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 $u$ , $v$ , $w$ , ...)	$- v 2 w u 2 + 2 v w u 2 - w u 2 + u 2 + 2 v u + 2 v 2 w u -2 v w u -2 u + v 2 -2 v - v 2 w + 1$ (db)
Jones polynomial	$q 3 -2 q 2 + 5 q -4 + 7 q -1 -6 q -2 + 5 q -3 -4 q -4 + 2 q -5$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$a 6 - z 4 a 4 -3 z 2 a 4 -2 a 4 + z 6 a 2 + 4 z 4 a 2 + 5 z 2 a 2 + a 2 z -2 + 3 a 2 -2 z 4 -6 z 2 -2 z -2 -4 + z 2 a -2 + a -2 z -2 + 2 a -2$ (db)
Kauffman polynomial	$a 2 z 8 + z 8 + 3 a 3 z 7 + 5 a z 7 + 2 z 7 a -1 + 3 a 4 z 6 + 4 a 2 z 6 + z 6 a -2 + 2 z 6 + a 5 z 5 -6 a 3 z 5 -13 a z 5 -6 z 5 a -1 -5 a 4 z 4 -17 a 2 z 4 -4 z 4 a -2 -16 z 4 + 3 a 5 z 3 + 7 a 3 z 3 + 6 a z 3 + 2 z 3 a -1 + 3 a 6 z 2 + 6 a 4 z 2 + 14 a 2 z 2 + 6 z 2 a -2 + 17 z 2 -2 a 5 z -6 a 3 z + 4 z a -1 - a 6 - a 4 -3 a 2 -4 a -2 -6-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 =

-2 is the signature of L10n71. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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