Operad: Dual Triduplicial

abbreviation

TriDup!

category

vec

type

non-symetrique

dimensions

1, 3, 7, 15, 31, 63, 127

OEIS: A000225

Formula: 2**n-1

Serie: 1/(1-2*x)-1/(1-x)

properties

binary, quadratic, Koszul

Koszul dual operad

TriDup

generateurs

• generator < of arity 2
• generator o of arity 2
• generator > of arity 2

relations

• equality: (x<y)<z = x<(y<z)
• equality: (xoy)oz = xo(yoz)
• equality: (x>y)>z = x>(y>z)
• equality: (x>y)<z = x>(y<z)
• equality: (xoy)<z = x<(y<z)
• equality: (x>y)oz = x>(yoz)
• equality: (xoy)>z = xo(y>z)
• relation: (x<y)>z
• relation: (x<y)oz
• relation: x<(y>z)
• relation: x<(yoz)

References

• J.-C. Novelli et J.-Y. Thibon, 2020 ↗ ↗