Some asymptotic bijections
type: Item
instance of: scholarly article
title: Some asymptotic bijections
zbMATH Open document ID: 0554.05004
DOI: 10.1016/0097-3165(85)90029-9
author: Edward A. Bender
author: Doron Zeilberger
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: Let \(S_ n\supseteq S_ n'\), \(T_ n\supseteq T_ n'\) with \(| S_ n| \sim | S_ n'|\) and \(| T_ n\sim | T_ n'|\) as \(n\to \infty\). If there exist bijections \(\Phi_ n\) from \(S_ n'\) to \(T_ n'\) then \(\Phi_ n\) is called an asymptotic bijection from \(S_ n\) to \(T_ n\). Using this idea, the authors verify the partition formula: \(B_ r=e^{-1}\sum^{\infty}_{r=0}k^ r/k!\) for the number of partitions of an r-set, as well as \(I_ r=e^{- 1/2}r!\sum^{\infty}_{k=0}\left( \begin{matrix} 2k\\ r\end{matrix} \right)/r!2^ k\), the number of involutions on an r-set.
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A10
zbMATH DE Number: 3882433
zbMATH Keywords: asymptotic bijection
zbMATH Keywords: partition formula
reviewed by: Ezra Brown
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90029-9
OpenAlex ID: W2003184453
cites work: Q4769056
cites work: An identity for fixed points of permutations
cites work: Q3243274
description: scientific article; zbMATH DE number 3882433