Spectrum of permanent's values and its extremal magnitudes in $\Lambda_n^3$ and $\Lambda_n(\alpha,\beta,\gamma)$

Abstract

Let $\Lambda_n^k$ 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 $\Lambda_n^k$ is not quite studied, is $k=3.$ We give a simple algorithm for calculation upper magnitudes of permanent in $\Lambda_n^3$ and consider some extremal problems in a generalized class $\Lambda_n(\alpha,\beta,\gamma),$ the matrices of which contain in each row and in each column nonzero elements $\alpha,\beta,\gamma$ and $n-3$ zeros.