Characterizing profiles of \(k\)-families in additive Macaulay posets
type: Item
instance of: scholarly article
title: Characterizing profiles of \(k\)-families in additive Macaulay posets
zbMATH Open document ID: 0887.06002
author: G. F. Clements
published in: Journal of Combinatorial Theory. Series A
publication date: 1998-05-06T00:00:00Z
review text: The famous theorem of Kruskal and Katona gives a complete characterization of \(f\)-vectors of simplicial complexes. A similar result for \textit{semisimplicial complexes} has been proved by F. S. Macaulay in 1927. In 1969 G. F. Clements and B. Lindström proved a ``\textit{generalized Macaulay theorem}'' which contains both the Kruskal-Katona and the Macaulay theorem as special cases. Later, further generalizations led the author to the notion of \textit{additive Macaulay posets} [Order 14, 39-46 (1997; Zbl 0884.05090)]. Here the author investigates some properties of these posets. Namely, a subset of a poset is a \textsl{\(k\)-family} if there is no chain consisting of \(k+1\) of its elements. A subset of a ranked poset consisting of \(p_i\) elements of rank \(i\) is said to have \textsl{profile} \((p_0, p_1,\ldots)\). A characterization is given for profiles of \(k\)-families in additive Macaulay posets.
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 1093105
zbMATH Keywords: additive Macaulay poset
zbMATH Keywords: antichain
zbMATH Keywords: profile
zbMATH Keywords: \(k\)-family
reviewed by: Valeriy B. Mnukhin
MaRDI profile type: Publication
full work available at URL: jcta.1997.2828
OpenAlex ID: W1977776922
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DOI: 10.1006/JCTA.1997.2828
description: scientific article; zbMATH DE number 1093105