Showing papers by "Richard A. Brualdi published in 2013"
TL;DR: In this paper, the zero-nonzero patterns of n × n alternating sign matrices are studied and the minimum term rank of these patterns is determined, and the maximum number of edges in such graphs is determined.
29 citations
TL;DR: This generalization of majorization in R n to a majorization order for functions defined on a partially ordered set P uses inequalities for partial sums associated with ideals in P .
7 citations
TL;DR: In this article, a class of matrices whose row and column sum vectors are majorized by given vectors b and c, and whose entries lie in the interval [0, 1] was considered.
Abstract: We consider a class of matrices whose row and column sum vectors are majorized by given vectors b and c, and whose entries lie in the interval [0, 1]. This class generalizes the class of doubly stochastic matrices. We investigate the corresponding polytope Ω(b|c) of such matrices. Main results include a generalization of the Birkhoff–von Neumann theorem and a characterization of the faces, including edges, of Ω(b|c).
6 citations
1 citations
Posted Content•
TL;DR: In this article, the first and last nonzero entries in each row and column are specified to be + 1 and − 1, respectively, and necessary and sufficient conditions for such matrices to exist.
Abstract: In alternating sign matrices the first and last nonzero entry in each row and column is specified to be +1.
Such matrices always exist. We investigate a generalization by specifying independently the sign of the first and last nonzero entry in each row and column to be either a +1 or a -1. We determine necessary and sufficient conditions for such matrices to exist.