Covering posets
type: Item
instance of: scholarly article
title: Covering posets
zbMATH Open document ID: 0654.06001
DOI: 10.1016/0012-365X(88)90099-4
author: Gerhard Behrendt
published in: Discrete Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let \((X,\leq)\) be an ordered set. A pair \((a,b)\) of elements of \(X\) is a covering pair if \(b\) covers \(a\). The set \(C(X)\) of all covering pairs of \(X\) can be naturally ordered by \((a,b)\leq (c,d)\) iff \((a,b)=(c,d)\) or \(b\leq c\). The poset \((C(X),\leq)\) is called the covering poset of \((X,\leq)\). The paper contains necessary and sufficient conditions for a finite poset to be a covering poset of a finite poset. The author also derives some relations between finite posets with isomorphic covering posets and some relations between dimensions of \((X,\leq)\) and \((C(X),\leq)\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 4066960
zbMATH Keywords: covering pairs
zbMATH Keywords: covering poset
zbMATH Keywords: dimensions
MaRDI profile type: Publication
cites work: Partially Ordered Sets
cites work: Complexity of diagrams
cites work: Q3291034
cites work: Q3764190
full work available at URL: 0012-365x(88)90099-4
OpenAlex ID: W2913232281
description: scientific article; zbMATH DE number 4066960