Faces of the polytope of doubly substochastic matrices
A doubly substochastic matrix is a square nonnegative matrix such that each row and each column sums at most one. The set of all \(n\times n\) doubly substochastic matrices forms a convex polytope \(\omega_{n}\) of dimension \(n^{2}\). The paper provides necessary and sufficient conditions for a face of \(\omega_{n}\) to be nonempty, and descriptions of all 1-dimensional faces, 2-dimensional faces, and facets of \(\omega_{n}\). It is worth to recall that \textit{R. A. Brualdi} and \textit{P. M. Gibson} [J. Comb. Theory, Ser. A 22, 194--230 (1977; Zbl 0355.15013)] characterised the faces of the polytope obtained from the set of all \(n\times n\) doubly stochastic matrix, square nonnegative matrices such that each row and each column sums to one.
scientific article; zbMATH DE number 7462788