The spider poset is Macaulay
type: Item
instance of: scholarly article
title: The spider poset is Macaulay
zbMATH Open document ID: 0951.06006
author: Sergej L. Bezrukov
author: Robert Elsässer
published in: Journal of Combinatorial Theory. Series A
publication date: 2000-07-09T00:00:00Z
review text: Let \(Q(k, \ell)\) be the partially ordered set whose Hasse diagram can be obtained from \(k+1\) copies of a chain with \(l+1\) vertices by identifying their top vertices. Let \(Q^n(k,\ell)\) be the \(n\)th cartesian power of \(Q(k,\ell)\). It is proved that \(Q^n(k,\ell)\) is a Macaulay poset for any positive integers \(k, \ell\) and \(n\). That is, there exists a (new) linear order on the ground set of \(Q^n(k,\ell)\) such that the shadow of the first \(m\) elements (\(m\) arbitrary) of any level consists of the first elements of the neighbouring level and has minimum size with respect to the shadow of any \(m\)-element subset of the given level.
reviewed by: Konrad Engel
Mathematics Subject Classification ID: 06A11
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 1443247
zbMATH Keywords: Macaulay poset
zbMATH Keywords: spider poset
zbMATH Keywords: Kruskal-Katona theorem
zbMATH Keywords: shadow minimization
zbMATH Keywords: Clements-Lindström theorem
MaRDI profile type: Publication
OpenAlex ID: W2090163613
cites work: Q4712283
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DOI: 10.1006/JCTA.1999.2994
description: scientific article; zbMATH DE number 1443247