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Operad: Arbustive

abbreviation
Arb
category
set
type
symetrique
dimensions

1, 3, 19, 195, 2791, 51303, 1152019, 30564075

OEIS: A048172

Serie: (log(1+x)-x**2/(1+x)).reverse()

Actions: s[1], s[1, 1] + 2*s[2], 2*s[1, 1, 1] + 6*s[2, 1] + 5*s[3], 5*s[1, 1, 1, 1] + 19*s[2, 1, 1] + 17*s[2, 2] + 28*s[3, 1] + 15*s[4], 13*s[1, 1, 1, 1, 1] + 64*s[2, 1, 1, 1] + 101*s[2, 2, 1] + 132*s[3, 1, 1] + 133*s[3, 2] + 128*s[4, 1] + 48*s[5], 35*s[1, 1, 1, 1, 1, 1] + 219*s[2, 1, 1, 1, 1] + 480*s[2, 2, 1, 1] + 310*s[2, 2, 2] + 581*s[3, 1, 1, 1] + 1118*s[3, 2, 1] + 415*s[3, 3] + 799*s[4, 1, 1] + 837*s[4, 2] + 568*s[5, 1] + 167*s[6]

properties
binary, quadratic, Koszul
generateurs
  • generator * of type s[1]**2
  • generator m of type s[2]
relations
  • equality: (xmy)mz = xm(ymz)
  • equality: (x*y)*z = (x*z)*y
  • equality: (x*y)*z = x*(ymz)
morphisms
→ Zin

References