Partitions of multisets. II
type: Item
instance of: scholarly article
title: Partitions of multisets. II
zbMATH Open document ID: 0553.05010
DOI: 10.1016/0012-365X(84)90029-3
author: Edward A. Bender
author: John S. Devitt
author: L. Bruce Richmond
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: [For part I see the paper of the first author, ibid. 9, 301-311 (1974; Zbl 0289.05014.] A multiset of type \(m\) is a multiset in which exactly \(m_ i\) distinct elements appear exactly \(i\) times. The number of partitions of a multiset of type \(m\) having exactly \(t\) blocks of size \(b\) is \(e^{-\gamma}\gamma^ t/t!+o(1)\) when \(M\to \infty,\), where \(M=\sum im_ i,\gamma =(\log s)^ b/b!\) and \(s \log s=M.\) This result extends an earlier result of \textit{J. Haigh} [J. Comb. Theory, Ser. A 13, 287--295 (1972; Zbl 0238.05003)].
Mathematics Subject Classification ID: 05A18
zbMATH DE Number: 3880712
zbMATH Keywords: multiset
zbMATH Keywords: partition numbers
reviewed by: T. Spircu
MaRDI profile type: Publication
cites work: Q5618377
cites work: Partitions of multisets
cites work: Asymptotic Methods in Enumeration
cites work: Q5549081
cites work: The Enumeration of Covers of a Finite Set
cites work: Random equivalence relations
cites work: Q3897059
full work available at URL: 0012-365x(84)90029-3
OpenAlex ID: W1979667972
description: scientific article; zbMATH DE number 3880712