On the Location of the Maximum Stirling Number(s) of the Second Kind

Abstract.

The Stirling number of the second kind S(n, k) is the number of ways of partitioning a set of n elements into k nonempty subsets. It is well known that the numbers S(n, k) are unimodal in k, and there are at most two consecutive values K _n such that (for fixed n) S(n,K _n ) is maximal. We determine numerical bounds for K _n , and our result shows that in many cases K _n can be uniquely determined.