AN UPPER BOUND FOR THE PERMANENT OF A NONNEGATIVE MATRIX

Let A be a fully indecomposable, nonnegative matrix of order n with ro w sums r(1),..., r(n), and let s(i) equal the smallest positive elemen t in row i of A. We prove the permanental inequality per(A) less than or equal to (i=1)Pi(n)S(i) + (i=1)Pi(n)(r(i)-s(i)) and characterize th e case of equality. In 1984 Donald, Elwin, Hager, and Salamon gave a g raph-theoretic proof of the special case in which A is a nonnegative i nteger matrix. (C) 1998 Elsevier Science Inc. All rights reserved.