An extremal problem for antichains of subsets of a multiset
type: Item
instance of: scholarly article
title: An extremal problem for antichains of subsets of a multiset
zbMATH Open document ID: 0607.05009
DOI: 10.1016/0012-365X(87)90146-4
author: G. F. Clements
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let F be a collection of subsets of a finite set S such that no member of F is contained in any other. Let \(\bar F\) denote the collection of all subsets of S containing a member of F as a subset, and let \b{F} denote the collection of all subsets of S contained in a member of F. Daykin has obtained the best possible upper bound for \(\min(\bar F,\underline F)\), taken over all such F, and has characterized all the extremal F. The author obtains the corresponding upper bound when the set S is replaced by a multiset, and also obtains partial results concerning the extremal cases. The proofs depend on several of the author's results on the generalized Macaulay theorem of Clements and Lindström.
Mathematics Subject Classification ID: 05A99
Mathematics Subject Classification ID: 05A20
zbMATH DE Number: 3981176
zbMATH Keywords: antichains
zbMATH Keywords: multiset
MaRDI profile type: Publication
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full work available at URL: 0012-365x(87)90146-4
OpenAlex ID: W2038621400
description: scientific article; zbMATH DE number 3981176