L10a61

(Knotscape image)

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

Visit L10a61's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_10,4,11,3 X_20,10,7,9 X₂₇₃₈ X_18,14,19,13 X_6,12,1,11 X_16,20,17,19 X_4,16,5,15 X_14,6,15,5 X_12,18,13,17
Gauss code	{1, -4, 2, -8, 9, -6}, {4, -1, 3, -2, 6, -10, 5, -9, 8, -7, 10, -5, 7, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 4 + u 4 -2 v 2 u 3 + 6 v u 3 -3 u 3 + 4 v 2 u 2 -9 v u 2 + 4 u 2 -3 v 2 u + 6 v u -2 u + v 2 - v$ (db)
Jones polynomial	$-q^{19/2}+4 q^{17/2}-7 q^{15/2}+11 q^{13/2}-14 q^{11/2}+14 q^{9/2}-14 q^{7/2}+10 q^{5/2}-7 q^{3/2}+3 \sqrt{q}-\frac{1}{\sqrt{q}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$- z 5 a -3 -2 z 5 a -5 + z 3 a -1 -5 z 3 a -5 + 3 z 3 a -7 + z a -1 + 3 z a -3 -6 z a -5 + 4 z a -7 - z a -9 + 2 a -3 z -1 -3 a -5 z -1 + a -7 z -1$ (db)
Kauffman polynomial	$- z 9 a -5 - z 9 a -7 -4 z 8 a -4 -8 z 8 a -6 -4 z 8 a -8 -5 z 7 a -3 -13 z 7 a -5 -14 z 7 a -7 -6 z 7 a -9 -3 z 6 a -2 + z 6 a -4 + 5 z 6 a -6 -3 z 6 a -8 -4 z 6 a -10 - z 5 a -1 + 9 z 5 a -3 + 33 z 5 a -5 + 34 z 5 a -7 + 10 z 5 a -9 - z 5 a -11 + 5 z 4 a -2 + 7 z 4 a -4 + 13 z 4 a -6 + 18 z 4 a -8 + 7 z 4 a -10 + 2 z 3 a -1 -8 z 3 a -3 -32 z 3 a -5 -28 z 3 a -7 -5 z 3 a -9 + z 3 a -11 -2 z 2 a -2 -7 z 2 a -4 -14 z 2 a -6 -12 z 2 a -8 -3 z 2 a -10 - z a -1 + 6 z a -3 + 15 z a -5 + 10 z a -7 + 2 z a -9 + 3 a -4 + 3 a -6 + a -8 -2 a -3 z -1 -3 a -5 z -1 - a -7 z -1$ (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 =

3 is the signature of L10a61. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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