Lower bounds on zero-one matrices

In this paper we work with pairs of zero-one matrices whose product is the full upper-triangular zero-one matrix. We establish a lower bound for the sum of the non-zero entries in them, using elementary concepts of linear algebra. With this algebraic method we reach the best possible lower bound, since pairs of such matrices may be found whose amount of non-zero entries is exactly our lower bound. (C) 2003 Elsevier Inc. All rights reserved.