Some applications of doubly stochastic matrices

Abstract

We discuss primarily two applications of doubly stochastic matrices and related matrices. The first concerns a topic in communication theory called satellite-switched, time-division multiple-access systems, and we attempt to illuminate some results which have occured in the engineering literature. The second concerns a recent notion of a doubly stochastic automorphism of a graph. We prove several new theorems about doubly stochastic automorphisms of certain classes of graphs, and in particular, obtain a theorem of which Birkhoff's theorem for doubly stochastic matrices is a special case.