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

الملخص EN

Let Λnk 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 Λnk is not quite studied, is k=3.

We give a simple algorithm for calculation of upper magnitudes of permanent in Λn3 and consider some extremal problems in a generalized class Λn(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.