Spectrum of Permanent’s Values and Its Extremal Magnitudes inΛn3andΛn(α,β,γ)

摘要

LetΛnkdenote the class of(0,1)square matrices containing in each row and in each column exactlyk1’s. The minimal value ofk, for which the behavior of the permanent inΛnkis not quite studied, isk=3. We give a simple algorithm for calculation of upper magnitudes of permanent inΛn3and consider some extremal problems in a generalized classΛn(α,β,γ), the matrices of which contain in each row and in each column nonzero elementsα,β, andγandn-3zeros.