L10n61

(Knotscape image)

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

Visit L10n61's page at the original Knot Atlas.

Planar diagram presentation	X_12,1,13,2 X_16,7,17,8 X_5,1,6,10 X₃₇₄₆ X_9,5,10,4 X_20,17,11,18 X_18,13,19,14 X_14,19,15,20 X_2,11,3,12 X_8,15,9,16
Gauss code	{1, -9, -4, 5, -3, 4, 2, -10, -5, 3}, {9, -1, 7, -8, 10, -2, 6, -7, 8, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$\frac{-2 u^3 v^2+2 u^3 v-u^3+2 u^2 v^2-2 u^2 v-2 u v^2+2 u v-v^3+2 v^2-2 v}{u^{3/2} v^{3/2}}$ (db)
Jones polynomial	$-\frac{6}{q^{9/2}}+\frac{5}{q^{7/2}}-\frac{7}{q^{5/2}}+\frac{5}{q^{3/2}}+\frac{1}{q^{15/2}}-\frac{2}{q^{13/2}}+\frac{4}{q^{11/2}}+2 \sqrt{q}-\frac{4}{\sqrt{q}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z a 7 -2 a 7 z -1 + 3 z 3 a 5 + 9 z a 5 + 7 a 5 z -1 -2 z 5 a 3 -9 z 3 a 3 -14 z a 3 -7 a 3 z -1 + 2 z 3 a + 4 z a + 2 a z -1$ (db)
Kauffman polynomial	$a 8 z 6 -4 a 8 z 4 + 5 a 8 z 2 -2 a 8 + 2 a 7 z 7 -7 a 7 z 5 + 7 a 7 z 3 -4 a 7 z + 2 a 7 z -1 + a 6 z 8 + 2 a 6 z 6 -17 a 6 z 4 + 20 a 6 z 2 -8 a 6 + 6 a 5 z 7 -20 a 5 z 5 + 22 a 5 z 3 -17 a 5 z + 7 a 5 z -1 + a 4 z 8 + 5 a 4 z 6 -24 a 4 z 4 + 29 a 4 z 2 -13 a 4 + 4 a 3 z 7 -12 a 3 z 5 + 18 a 3 z 3 -16 a 3 z + 7 a 3 z -1 + 4 a 2 z 6 -11 a 2 z 4 + 17 a 2 z 2 -8 a 2 + a z 5 + 3 a z 3 -3 a z + 2 a z -1 + 3 z 2 -2$ (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 =

-1 is the signature of L10n61. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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