Set partition asymptotics and a conjecture of Gould and Quaintance

Walaa Asakly, Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour, Stephan Wagner

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)672-682
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume416
Issue number2
DOIs
StatePublished - 15 Aug 2014

Keywords

  • Asymptotics
  • Bell numbers
  • Generating functions
  • Set partitions

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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