Sparse anti-magic squares and vertex-magic labelings of bipartite graphs

A sparse anti-magic square is an n X n array whose non-zero entries are the consecutive integers 1,...,m for some m ≤ n² and whose row-sums and column-sums form a set of consecutive integers: We derive some basic properties of these arrays and provide constructions for several infinite families of them. Our main interest in these arrays is their application to constructing vertex-magic labelings for bipartite graphs.