An upper bound for the permanent of a nonnegative matrix Original Research Article

Let A be a fully indecomposable, nonnegative matrix of order n with row sums rl,rn, and let si equal the smallest positive element in row i of A. We prove the permanental inequality image and characterize the case of equality. In 1984 Donald, Elwin, Hager, and Salamon gave a graph-theoretic proof of the special case in which A is a nonnegative integer matrix.