Set partition asymptotics and a conjecture of Gould and Quaintance

Abstract

The main result of this paper is the generalization and proof of a conjecture by Gould and Quaintance on the asymptotic behavior of certain sequences related to the Bell numbers. Thereafter we show some applications of the main theorem to statistics of partitions of a finite set S, i.e., collections B1,B2,…,Bk of non-empty disjoint subsets of S such that ⋃i=1kBi=S, as well as to certain classes of partitions of [n].