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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 960182, 6 pages
http://dx.doi.org/10.1155/2015/960182
Research Article

On Factorizations of Upper Triangular Nonnegative Matrices of Order Three

Department of Mathematics, Huizhou University, Huizhou, Guangdong 516007, China

Received 2 February 2015; Revised 18 March 2015; Accepted 18 March 2015

Academic Editor: Ivan Area

Copyright © 2015 Yi-Zhi Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let denote the semigroup of upper triangular matrices with nonnegative integral-valued entries. In this paper, we investigate factorizations of upper triangular nonnegative matrices of order three. Firstly, we characterize the atoms of the subsemigroup of the matrices in with nonzero determinant and give some formulas. As a consequence, problems 4a and 4c presented by Baeth et al. (2011) are each half-answered for the case . And then, we consider some factorization cases of matrix in with and give formulas for the minimum factorization length of some special matrices in .