L10n36

(Knotscape image)

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

Visit L10n36's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_3,13,4,12 X_16,13,17,14 X_14,9,15,10 X_10,15,11,16 X_17,5,18,20 X_7,19,8,18 X_19,9,20,8 X₂₅₃₆ X_11,1,12,4
Gauss code	{1, -9, -2, 10}, {9, -1, -7, 8, 4, -5, -10, 2, 3, -4, 5, -3, -6, 7, -8, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	0 (db)
Jones polynomial	$q^{9/2}-q^{7/2}+q^{5/2}-q^{3/2}-\sqrt{q}-\frac{1}{\sqrt{q}}-\frac{1}{q^{3/2}}+\frac{1}{q^{5/2}}-\frac{1}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a z 5 - z 5 a -1 - a 3 z 3 + 6 a z 3 -6 z 3 a -1 + z 3 a -3 -3 a 3 z + 11 a z -11 z a -1 + 3 z a -3 -2 a 3 z -1 + 7 a z -1 -7 a -1 z -1 + 2 a -3 z -1$ (db)
Kauffman polynomial	$- a 3 z 7 - a z 7 - z 7 a -1 - z 7 a -3 - a 4 z 6 -2 a 2 z 6 -2 z 6 a -2 - z 6 a -4 -2 z 6 + 5 a 3 z 5 + 7 a z 5 + 7 z 5 a -1 + 5 z 5 a -3 + 5 a 4 z 4 + 12 a 2 z 4 + 12 z 4 a -2 + 5 z 4 a -4 + 14 z 4 -6 a 3 z 3 -14 a z 3 -14 z 3 a -1 -6 z 3 a -3 -6 a 4 z 2 -18 a 2 z 2 -18 z 2 a -2 -6 z 2 a -4 -24 z 2 + 4 a 3 z + 14 a z + 14 z a -1 + 4 z a -3 + 2 a 4 + 8 a 2 + 8 a -2 + 2 a -4 + 13-2 a 3 z -1 -7 a z -1 -7 a -1 z -1 -2 a -3 z -1$ (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 =

0 is the signature of L10n36. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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