ON THE EXISTENCE OF SEQUENCES AND MATRICES WITH PRESCRIBED PARTIAL-SUMS OF ELEMENTS

We prove necessary and sufficient conditions for the existence of sequ ences and matrices with elements in given intervals and with prescribe d lower and upper bounds on the element sums corresponding to the sets of an orthogonal pair of partitions. We use these conditions to gener alize known results on the existence of nonnegative matrices with a gi ven zero pattern and prescribed row and column sums. We also generaliz e recently proven results on the existence of (a real or nonnegative) square matrix A With a given zero pattern and With prescribed row sums such that A + A(T) is prescribed. We also introduce Hadamard adjustme nts, by means of which we generalize known results on the scaling of m atrices with a given pattern to achieve prescribed row and column sums . (C) 1997 Elsevier Science Inc.