Some limit theorems with respect to constrained permutations and partitions
type: Item
instance of: scholarly article
title: Some limit theorems with respect to constrained permutations and partitions
zbMATH Open document ID: 1356.05011
author: Chenying Wang
author: István Mező
published in: Monatshefte für Mathematik
publication date: 2017-01-25T00:00:00Z
review text: In this paper, it is shown that for fixed positive integers \(k\) and \(m\) the number of permutations on \(n\) elements where the number of cycles in the permutations is \(k\) (\(k\)-permutations for short) is asymptotically equal (for \(n\rightarrow \infty\)) to the number of \(k\)-permutations on \(n\) elements such that all the \(k\) cycles contain at least \(m\) elements. This property also holds for the number of partitions of \(n\) elements into \(k\) subsets and the number of partitions of \(n\) elements into \(k\) subsets such that each block contains at least \(m\) elements. Finally, the exact asymptotics for the number of partitions of \(n\) elements such that each block contains at least \(m\) elements was deduced by using the classical method of Hayman.
reviewed by: Ioan Tomescu
Mathematics Subject Classification ID: 05A16
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 11B73
zbMATH DE Number: 6677802
zbMATH Keywords: set partitions
zbMATH Keywords: restricted set partitions
zbMATH Keywords: associated Stirling numbers
zbMATH Keywords: Bell numbers
zbMATH Keywords: asymptotics
MaRDI profile type: Publication
full work available at URL: s00605-015-0855-z
OpenAlex ID: W2256194434
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DOI: 10.1007/S00605-015-0855-Z
description: scientific article; zbMATH DE number 6677802