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Operad: Non-Associative Permutative

abbreviation
NAP
category
set
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: P-x*exp(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
Koszul dual operad
NAP!
generateurs
  • generator * of type s[1]**2
relations
  • equality: (x*y)*z = (x*z)*y
morphisms
→ Zin, → Perm, → Arb

References