A solution to an inverse height and level characteristics problem

Abstract

strictly majorizes a when reordered in non-increasing order. We introduce a new algorithm that constructs a graph G such that every matrix with graph G satisfies the requirements. Our algorithm does not use the machinery of the Gale-Ryser Theorem on the existence of a 0-1 matrix with given row and column sums, used in [4] and [I]. Also, our algorithm results in a matrix of size lower than the size of the matrix constructed in [I]. By that, we partially answer a question asked in [I]. Most of our notation and definitions are contained in Section 2. The results are brought in Section