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Operad: Post-Lie

abbreviation
PostLie
category
vec
type
symetrique
dimensions

1, 3, 20, 210, 3024, 55440

OEIS: A006963

Formula: lambda n: 1 if n == 1 else factorial(2*n-1)/factorial(n)

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

properties
Koszul, binary, quadratic
Koszul dual operad
ComTrias
generateurs
  • generator c of type s[1,1]
  • generator > of type s[1]**2
relations
  • relation: (xcy)cz+(ycz)cx+(zcx)cy
  • equality: x>(ycz) = (x>y)cz + yc(x>z)
  • equality: (xcy)>z = x>(y>z)-(x>y)>z - y>(x>z) + (y>x)>z
morphisms
→ PreLie

References