Showing papers by "Richard A. Brualdi published in 2005"
TL;DR: A sign-nonsingular matrix of order n (n + 1) whose determinant gives Πn, whose calculation is reduced to that of a Hankel matrix oforder n whose entries are large Schroder numbers is determined.
62 citations
TL;DR: In this article, a Bruhat order for the class of m by n (0, 1)-matrices with a given row and column sum vector is defined, and an algorithm is given for constructing a minimal matrix (with respect to the Bruhat ordering) in such a class.
Abstract: Generalizing the Bruhat order for permutations (so for permutation matrices), a Bruhat order is defined for the class of m by n (0, 1)-matrices with a given row and column sum vector. An algorithm is given for constructing a minimal matrix (with respect to the Bruhat order) in such a class. This algorithm simplifies in the case that the row and column sums are all equal to a constant k .W henk =2o rk = 3, all minimal matrices are determined. Examples are presented that suggest such a determination might be very difficult for k ≥ 4.
20 citations
TL;DR: An algorithm is given to construct such a matrix which is based on three applications of the well-known Gale-Ryser algorithm for constructing (0, 1)-matrices with given line sums with a characterization in terms of a certain “structure matrix”.
10 citations