Engel's inequality for Bell numbers
type: Item
instance of: scholarly article
title: Engel's inequality for Bell numbers
zbMATH Open document ID: 0830.11010
DOI: 10.1016/0097-3165(95)90033-0
author: E. Rodney Canfield
published in: Journal of Combinatorial Theory. Series A
publication date: 1995-10-04T00:00:00Z
review text: \textit{K. Engel} [J. Comb. Theory, Ser. A 65, No. 1, 67-78 (1994; Zbl 0795.05051)]\ conjectured that \(\tau_n= (B_{n+ 1}/ B_n) -1\) (\(B_n\) the \(n\)-th Bell number; \(\tau_n\) the average number of blocks in a partition of an \(n\)-set) is concave. The author proves the conjecture for all \(n\) sufficiently large, using the asymptotic formula for Bell numbers of Moser and Wyman. He also shows that the average number of singleton blocks in a partition of an \(n\)-set is an increasing function of \(n\).
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 05A18
zbMATH DE Number: 802354
zbMATH Keywords: Engel's inequality
zbMATH Keywords: Bell number
zbMATH Keywords: partition
zbMATH Keywords: \(n\)-set
reviewed by: Gerald L. Alexanderson
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90033-0
OpenAlex ID: W1987029529
Wikidata QID: Q56157590
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description: scientific article; zbMATH DE number 802354