Together with Marco Timpanella (University of Perugia) and Giovanni Zini (University of Modena and Reggio Emilia), the research group organize monthly seminars.
15 January 2026 [4.00 pm - Italian time] - Lorenzo Mella (Università degli Studi di Brescia, Italia)
Title: The Hadamard quasigroup product and Orthogonal Arrays
Abstract: The Hadamard quasigroup product is an operation between arrays introduced in 2023 by Falcón et al. Given a Latin square L, the Hadamard quasigroup product between two arrays A and B is the array whose (i,j)-th entry is L(aij,bij).
In this talk, we first investigate some basic algebraic properties of the Hada mard quasigroup product. We then highlight a natural connection between this operation and the theory of orthogonal arrays and Latin squares. Finally, we introduce a multiary generalization of the Hadamard product, that is studied over m-ary operations on a finite set. This is a joint work with R. M. Falcón and P. Vojtěchovský.