OPERADS FOR n - ARY ALGEBRAS – CALCULATIONS AND CONJECTURES

In [8] we studied Koszulity of a family tAssd of operads depending on a natural number n ∈ N and on the degree d ∈ Z of the generating operation. While we proved that, for n ≤ 7, the operad tAssd is Koszul if and only if d is even, and while it follows from [4] that tAssd is Koszul for d even and arbitrary n, the (non)Koszulity of tAssd for d odd and n ≥ 8 remains an open problem. In this note we describe some related numerical experiments, and formulate a conjecture suggested by the results of these computations.