Abstract
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 per(A)⩽∏i=1nsi+∏i=1n(ri−si) 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.
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