Log-Concavity and the Exponential Formula

A 1996 result of Bender and Canfield showed that passing a log-concave sequence through the exponential formula resulted in a log-concave sequence which was almost log-convex. We generalize that result toq–log-concavity. Our proof follows Bender and Canfield for one part. For the other part, we use the theory of symmetric functions to show that the second part of the Bender–Canfield result follows directly from the first part. We also give several corollaries and examples.