Some nontrivial permanental mates (Q923670)

A pair of doubly stochastic matrices A, B is called a permanental pair if \(per[tA+(1-t)B]\) is a constant function of t for \(0\leq t\leq 1\). Conditions are given so that a pair A,B of doubly stochastic matrices be a permanental pair. The matrix B need not be permutation equivalent to A for this to be so. This resolves a question posed by \textit{E. T. H. Wang} [Amer. Math. Monthly 85, 188-190 (1978; Zbl 0378.15004)]. Two conjectures and a problem are stated at the end of the paper.