L10a76

(Knotscape image)

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

Visit L10a76's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_14,9,15,10 X₆₇₁₈ X_20,15,7,16 X_16,6,17,5 X_4,20,5,19 X_10,4,11,3 X_12,17,13,18 X_18,11,19,12 X_2,14,3,13
Gauss code	{1, -10, 7, -6, 5, -3}, {3, -1, 2, -7, 9, -8, 10, -2, 4, -5, 8, -9, 6, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + v u 4 + 4 v 2 u 3 -7 v u 3 + 2 u 3 -5 v 2 u 2 + 11 v u 2 -5 u 2 + 2 v 2 u -7 v u + 4 u + v -1$ (db)
Jones polynomial	$-q^{7/2}+4 q^{5/2}-9 q^{3/2}+12 \sqrt{q}-\frac{17}{\sqrt{q}}+\frac{17}{q^{3/2}}-\frac{16}{q^{5/2}}+\frac{13}{q^{7/2}}-\frac{8}{q^{9/2}}+\frac{4}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 -2 a 3 z 5 + 4 a z 5 - z 5 a -1 + a 5 z 3 -5 a 3 z 3 + 7 a z 3 -2 z 3 a -1 + a 5 z -4 a 3 z + 6 a z -2 z a -1 - a 3 z -1 + 3 a z -1 -2 a -1 z -1$ (db)
Kauffman polynomial	$-3 a 3 z 9 -3 a z 9 -7 a 4 z 8 -15 a 2 z 8 -8 z 8 -7 a 5 z 7 -9 a 3 z 7 -10 a z 7 -8 z 7 a -1 -4 a 6 z 6 + 8 a 4 z 6 + 29 a 2 z 6 -4 z 6 a -2 + 13 z 6 - a 7 z 5 + 11 a 5 z 5 + 28 a 3 z 5 + 32 a z 5 + 15 z 5 a -1 - z 5 a -3 + 6 a 6 z 4 + a 4 z 4 -17 a 2 z 4 + 5 z 4 a -2 -7 z 4 + a 7 z 3 -5 a 5 z 3 -23 a 3 z 3 -28 a z 3 -10 z 3 a -1 + z 3 a -3 -2 a 6 z 2 -3 a 4 z 2 - a 2 z 2 + 2 a 5 z + 7 a 3 z + 10 a z + 5 z a -1 + a 4 + 3 a 2 + 3- a 3 z -1 -3 a z -1 -2 a -1 z -1$ (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 =

-1 is the signature of L10a76. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -2$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -1$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 0$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{10}$
$r = 1$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{6}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$