Set partition asymptotics and a conjecture of Gould and Quaintance

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Asakly, Walaa¹  Blecher, Aubrey²  Brennan, Charlotte³  Knopfmacher, Arnold³  Mansour, Toufik¹  Wagner, Stephan⁴ 

[1] Univ Haifa, Dept Math, IL-3498838 Haifa, Israel

[2] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, South Africa

[3] Univ Witwatersrand, Sch Math, John Knopfmacher Ctr Applicable Anal & Number The, ZA-2050 Johannesburg, South Africa

[4] Univ Stellenbosch, Dept Math Sci, ZA-7602 Matieland, South Africa

关键词: Set partitions;    Generating functions;    Asymptotics;    Bell numbers;   

DOI  :  10.1016/j.jmaa.2014.02.061

来源: Elsevier

【 摘 要 】

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 B-1,B-2, ..., B-k of non-empty disjoint subsets of S such that U-i=1(k) B-i = S, as well as to certain classes of partitions of [n]. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free