Patterns that allow given row and column sums Original Research Article

The zero–nonzero patterns occurring among m-by-n matrices with given row and column sums are characterized. A (simple) “weak” version of this problem is also studied, and the solution to the “strong” problem is based, in part, on a theory of totally nonzero solutions to a linear system. Some motivation is provided by the question of patterns that allow commuting matrices. A corresponding problem for sign patterns is studied elsewhere.