Spectrum of Permanent’s Values and Its Extremal Magnitudes in Λn3 and Λ_n(α, β, γ)

Let (Formula presented.) denote the class of (0,1) square matrices containing in each row and in each column exactly k 1’s. The minimal value of k, for which the behavior of the permanent in (Formula presented.) is not quite studied, is k = 3. We give a simple algorithm for calculation of upper magnitudes of permanent in (Formula presented.) and consider some extremal problems in a generalized class Λ_n(α, β, γ), the matrices of which contain in each row and in each column nonzero elements α, β, and γ and n − 3 zeros.