logo of Operadia Operadia

Operad: Dual Quadri-algebra

abbreviation
Quad!
category
vec
type
non-symetrique
dimensions

1, 4, 9, 16, 25

OEIS: A000290

Formula: n**2

Serie: x*(1+x)/(1-x)**3

properties
binary, quadratic, Koszul, cyclic
Koszul dual operad
Quad
generateurs
  • generator ↖ of arity 2
  • generator ↗ of arity 2
  • generator ↘ of arity 2
  • generator ↙ of arity 2
relations
  • equality: (x↖y)↖z = x↖(y↖z)
  • equality: (x↖y)↖z = x↖(y↗z)
  • equality: (x↖y)↖z = x↖(y↘z)
  • equality: (x↖y)↖z = x↖(y↙z)
  • equality: (x↗y)↖z = x↗(y↖z)
  • equality: (x↗y)↖z = x↗(y↙z)
  • equality: (x↖y)↗z = x↗(y↘z)
  • equality: (x↗y)↗z = x↗(y↘z)
  • equality: (x↗y)↗z = x↗(y↗z)
  • equality: (x↙y)↖z = x↙(y↖z)
  • equality: (x↙y)↖z = x↙(y↗z)
  • equality: (x↘y)↖z = x↘(y↖z)
  • equality: (x↙y)↗z = x↘(y↗z)
  • equality: (x↘y)↗z = x↘(y↗z)
  • equality: (x↖y)↙z = x↙(y↙z)
  • equality: (x↖y)↙z = x↖(y↘z)
  • equality: (x↙y)↙z = x↙(y↙z)
  • equality: (x↘y)↙z = x↘(y↙z)
  • equality: (x↗y)↙z = x↘(y↙z)
  • equality: (x↘y)↘z = x↘(y↘z)
  • equality: (x↖y)↘z = x↘(y↘z)
  • equality: (x↗y)↘z = x↘(y↘z)
  • equality: (x↙y)↘z = x↘(y↘z)

References