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Operad: Zinbiel

abbreviations
Zin, Zinb
category
vec
type
symetrique
dimensions

1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800

OEIS: A000142

Formula: factorial(n)

Serie: x/(1-x)

Actions: s[1], s[1, 1] + s[2], s[1, 1, 1] + 2*s[2, 1] + s[3], s[1, 1, 1, 1] + 3*s[2, 1, 1] + 2*s[2, 2] + 3*s[3, 1] + s[4], s[1, 1, 1, 1, 1] + 4*s[2, 1, 1, 1] + 5*s[2, 2, 1] + 6*s[3, 1, 1] + 5*s[3, 2] + 4*s[4, 1] + s[5], s[1, 1, 1, 1, 1, 1] + 5*s[2, 1, 1, 1, 1] + 9*s[2, 2, 1, 1] + 5*s[2, 2, 2] + 10*s[3, 1, 1, 1] + 16*s[3, 2, 1] + 5*s[3, 3] + 10*s[4, 1, 1] + 9*s[4, 2] + 5*s[5, 1] + s[6]

properties
Koszul, binary, quadratic, anticyclic
Koszul dual operad
Leib
generateurs
  • generator < of type s[1]**2
relations
  • equality: (x<y)<z = x<(y<z)+x<(z<y)

References