Operad: Diassociative

abbreviation

Dias

category

set

type

non-symetrique

dimensions

1, 2, 3, 4, 5, 6, 7, 8, 9

OEIS: A000027

Formula: n

Serie: x/(1-x)**2

Equation: (1-x)**2*P-x

properties

Koszul, binary, quadratic, anticyclic

Koszul dual operad

Dend

generateurs

• generator ⊣ of arity 2
• generator ⊢ of arity 2

relations

• equality: (x⊣y)⊣z = x⊣(y⊣z)
• equality: (x⊣y)⊣z = x⊣(y⊢z)
• equality: (x⊢y)⊣z = x⊢(y⊣z)
• equality: (x⊣y)⊢z = x⊢(y⊢z)
• equality: (x⊢y)⊢z = x⊢(y⊢z)

morphisms

→ Perm, → As, → Trias

References

• J.-L. Loday, 2001 ↗