Sinkhorn, Richard2022-01-272022-01-27197213683946https://hdl.handle.net/10657/8624The purpose of this dissertation is to examine the structural properties of matrices whose entries are either 0 or 1. There are three main results. In Theorem 1, the author shows that the maximal number of positive entries (arcs) in an n x n nearly reducible matrix (minimally connected graph with n vertices) is 2(n - 1) and the matrix has a canonical form. In Theorem 2, he argues that the maximal number of positive entries in a nearly decomposable n x n matrix is 3(n - 1) and is obtained uniquely at a canonical matrix. In Theorem 3, he examines the structure of those nearly decomposable (0,l)-matrices whose permanent equals [sigma](A) - 2n + 2 where [sigma](A) is the number of positive entries in A.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital