Operad: Poisson

abbreviations

Pois, Poiss

category

Zvec

type

symetrique

dimensions

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

OEIS: A000142

Formula: factorial(n)

Serie: x/(1-x)

properties

Koszul, binary, quadratic, cyclic

Koszul dual operad

Pois

generateurs

• generator * of type s[2] of degree 0
• generator c of type s[1, 1] of degree 1

relations

• equality: (x*y)*z = x*(y*z)
• equality: xc(y*z) = (xcy)*z+y*(xcz)
• relation: (xcy)cz+(ycz)cx+(zcx)cy

morphisms

→ Com, → Lie, → Ram

References

• B. Fresse, 2006 ↗