The doubly graded matrix cone and Ferrers matrices

In this paper a doubly graded matrix refers to a nonnegative matrix where each row and each column is nonincreasing. The paper discusses different questions related to doubly graded matrices. We study the polyhedral cone consisting of all doubly graded matrices of size m×n. The faces are determined and related to Ferrers matrices. Different subsets of are investigated. The problem of the existence of an integral doubly graded matrix with given line sums is also studied.