Maximum permanents on certain classes of nonnegative matrices (Q913888)

The author shows that the maximum value of the permanent in a set \(U_ R(a,b)\) equals its maximum value in the convex hull of this set. \(U_ R(a,b)\) is the set of square matrices with each entry either a or b, where a,b are nonnegative, and having row sum vector R. This is used to generalize the upper bound on the permanent obtained by \textit{H. Minc} [Bull. Am. Math. Soc. 69, 789-791 (1963; Zbl 0116.252)] and \textit{L. M. Brégman} [Dokl. Akad. Nauk SSSR 211, 27-30 (1973; Zbl 0293.15010)].