Enumerating nested and consecutive partitions
type: Item
instance of: scholarly article
title: Enumerating nested and consecutive partitions
zbMATH Open document ID: 0819.05005
DOI: 10.1016/0097-3165(95)90097-7
published in: Journal of Combinatorial Theory. Series A
publication date: 1995-05-11T00:00:00Z
review text: The authors prove formulas for the number of partitions of an ordered set of \(n\) objects into \(p\) parts. For nested partitions \[ \text{N}(n, p)= {1\over n}\Biggl({n\atop p}\Biggr)\Biggl({n\atop p-1}\Biggr). \] For order-consecutive partitions \[ \text{OCP}(n, p)= \sum^{p-1}_{j= 0} \Biggl({n-1\atop 2p-j-2}\Biggr) \Biggl({2p-j- 2\atop j}\Biggr). \] For order-consecutive partition sequences \[ \text{OCPS}(n, p)= \sum^{p- 1}_{k= 0} (-1)^{p- 1-k} \Biggl({p-1\atop k}\Biggr) \Biggl({n+ 2k- 1\atop 2k}\Biggr). \] Properties of \(\text{N}(n, p)\) are discussed.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 753622
zbMATH Keywords: consecutive partitions
zbMATH Keywords: number of partitions
zbMATH Keywords: ordered set
zbMATH Keywords: nested partitions
zbMATH Keywords: order-consecutive partitions
author: Frank K. Hwang
author: Colin L. Mallows
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90097-7
OpenAlex ID: W2098780983
cites work: Structured Partitioning Problems
cites work: On clustering problems with connected optima in Euclidean spaces
cites work: Technical Note—A Partitioning Problem with Additive Objective with an Application to Optimal Inventory Groupings for Joint Replenishment
cites work: Consecutive Optimizers for a Partitioning Problem with Applications to Optimal Inventory Groupings for Joint Replenishment
cites work: Optimal partitions
cites work: Optimal Set Partitioning
cites work: Valency enumeration of rooted plane trees
description: scientific article; zbMATH DE number 753622