Products of elementary doubly stochastic matrices

While studying a theorem of Westwerk on higher numerical ranges, we became interested in how the theory of elementary doubly stochastic (e.d.s.) matrices is related to a result of Goldberg and Straus. We show that there exist classes of doubly stochastic (d.s.) matrices of order n≧3 and orthostochastic (o s) matrices of order n≧4 such that the matrices in these classes cannot be represented as a product of e.d.s. matrices. In fact the matrices in these classes do not admit a representation as an infinite limit of a product of e.d.s. matrices.