Paper detail

Spectrum of permanent's values and its extremal magnitudes in $Λ_n^3$ and $Λ_n(α,β,γ)$

Let $Λ_n^k$ 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 $Λ_n^k$ is not quite studied, is $k=3.$ We give a simple algorithm for calculation upper magnitudes of permanent in $Λ_n^3$ 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 $α,β,γ$ and $n-3$ zeros.