Some Inequalities involving (r!)1/r

Abstract

In a recent investigation of a conjecture on an upper bound for permanents of (0, 1)-matrices (2) we obtained some inequalities involving the function (r!)1/r which are of interest in themselves. Probably the most interesting of them, and certainly the hardest to prove, is the inequalitywhere ø(r = (r!)1/r. In the present paper we prove (1) and other inequalities involving the function ø(r.