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Operad: Pre-Lie

abbreviation
PreLie
category
vec
type
symetrique
dimensions

1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721, 1000000000

OEIS: A000169

Formula: n**(n - 1)

Serie: (x * exp(-x)).reverse()

Equation: x*(1-P)*diff(P,x)-P

Actions: s[1], s[1, 1] + s[2], s[1, 1, 1] + 3*s[2, 1] + 2*s[3], 2*s[1, 1, 1, 1] + 7*s[2, 1, 1] + 5*s[2, 2] + 9*s[3, 1] + 4*s[4], 4*s[1, 1, 1, 1, 1] + 17*s[2, 1, 1, 1] + 24*s[2, 2, 1] + 30*s[3, 1, 1] + 28*s[3, 2] + 26*s[4, 1] + 9*s[5], 8*s[1, 1, 1, 1, 1, 1] + 42*s[2, 1, 1, 1, 1] + 83*s[2, 2, 1, 1] + 49*s[2, 2, 2] + 96*s[3, 1, 1, 1] + 170*s[3, 2, 1] + 59*s[3, 3] + 117*s[4, 1, 1] + 114*s[4, 2] + 75*s[5, 1] + 20*s[6]

properties
Koszul, binary, quadratic, anticyclic, NielsenSchreier
Koszul dual operad
Perm
generateurs
  • generator < of type s[1]**2
relations
  • equality: (x<y)<z-x<(y<z) = (x<z)<y-x<(z<y)
morphisms
→ Dend, → Brace, → Novikov, → L-dend, → As, → NAP!

References