A canonical construction for nonnegative integral matrices with given line sums.

Let p be a positive integer and let A ( p ) ( R , S ) be the class of nonnegative integral matrices with entries less than or equal to p , with row–sum partition R , and column–sum partition S . In this paper we state a new necessary and sufficient condition for A ( p ) ( R , S ) ≠ ∅ . This condition generalizes the well known Gale–Ryser theorem. We also present a canonical construction for matrices in A ( p ) ( R , S ) . [ABSTRACT FROM AUTHOR]