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Operad: Yamaguti

abbreviation
Yam
category
vec
type
non-symetrique
dimensions

1, 1, 3, 6, 15, 36, 91, 232, 603, 1585, 4213, 11298

OEIS: A005043

Serie: -1/2*(2*x^2 + x + sqrt(-3*x^2 - 2*x + 1) - 1)/(x^3 + x^2)

properties
cyclic
generateurs
  • generator * of arity 2
  • generator ∧ of arity 3
  • generator ∨ of arity 3
relations
  • relation: (x*y)*z - x*(y*z) + x∧y∧z - x∨y∨z
  • equality: (x*y)∧z∧t = x∧(y*z)∧t
  • equality: x∧y∧(z*t) = (x∧y∧z)*t
  • equality: (x*y)∨z∨t = x*(y∨z∨t)
  • equality: x∨(y*z)∨t = x∨y∨(z*t)
  • equality: x*(y∧z∧t) = (x∨y∨z)*t
  • equality: (x∧y∧z)∧t∧u = x∧(y∨z∨t)∧u
  • equality: x∧(y∨z∨t)∧u = x∧y∧(z∧t∧u)
  • equality: x∧(y∧z∧t)∧u = (x∨y∨z)∧t∧u
  • equality: (x∨y∨z)∨t∨u = x∨(y∧z∧t)∨u
  • equality: x∨(y∧z∧t)∨u = x∨y∨(z∨t∨u)
  • equality: x∨(y∨z∨t)∨u = x∨y∨(z∧t∧u)
  • equality: x∧y∧(z∨t∨u) = (x∧y∧z)∨t∨u

References