Operad: Commutative-Magmatic

abbreviations

ComMag, Griess

category

set

type

symetrique

dimensions

1, 1, 3, 15, 105

OEIS: A001147

Formula: ZZ(2*n-3).multifactorial(2)

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

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

Actions: s[1], s[2], s[2, 1] + s[3], s[2, 1, 1] + 2*s[2, 2] + 2*s[3, 1] + 2*s[4], s[2, 1, 1, 1] + 4*s[2, 2, 1] + 4*s[3, 1, 1] + 6*s[3, 2] + 6*s[4, 1] + 3*s[5], s[2, 1, 1, 1, 1] + 6*s[2, 2, 1, 1] + 7*s[2, 2, 2] + 7*s[3, 1, 1, 1] + 21*s[3, 2, 1] + 8*s[3, 3] + 14*s[4, 1, 1] + 21*s[4, 2] + 14*s[5, 1] + 6*s[6]

properties

binary, quadratic, Koszul, free

Koszul dual operad

ComMag!

generateurs

• generator * of type s[2]

relations

morphisms

→ Com, → level, → PreLie, → Mag

References