logo of Operadia Operadia

Operad: Tridendriforme

abbreviation
Tridend
category
Zvec
type
non-symetrique
dimensions

1, 3, 11, 45, 197

OEIS: A001003

Serie: -(-1+3*x+sqrt(1-6*x+x**2))/(4*x)

Equation: P-x*(1+P)*(1+2*P)

properties
binary, quadratic, Koszul
Koszul dual operad
Trias
generateurs
  • generator < of arity 2
  • generator * of arity 2
  • generator > of arity 2
relations
  • equality: (x<y)<z = x<(y<z)+x<(y>z)+x<(y*z)
  • equality: (x>y)<z = x>(y<z)
  • equality: (x>y)>z+(x<y)>z+(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)
morphisms
→ CTD, → Dend

References