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].
Original language | English |
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Pages (from-to) | 672-682 |
Number of pages | 11 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 416 |
Issue number | 2 |
DOIs | |
State | Published - 15 Aug 2014 |
Keywords
- Asymptotics
- Bell numbers
- Generating functions
- Set partitions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics