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Operad: Triassociative

abbreviation
Trias
category
set
type
non-symetrique
dimensions

1, 3, 7, 15, 31, 63, 127, 255, 511

OEIS: A000225

Formula: 2**n-1

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

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

properties
binary, quadratic, Koszul
Koszul dual operad
Tridend
generateurs
  • 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)
morphisms
→ As, → Pasc

References