Inequalities for the gamma function with applications to permanents Original Research Article

The best known upper bound on the permanent of a 0–1 matrix relies on the knowledge of the number of nonzero entries per row. In certain applications only the total number of nonzero entries is known. In order to derive bounds in this situation we prove that the function f:(−1, ∞) → R, defined by f (x):= (log ⌈(x + 1))/x, is concave, strictly increasing and satisfies an analogue of the famous Bohr-Mollerup theorem. For further discussion of such bounds we derive some inequalities for this function.