A note on linear extensions and incomparable pairs
type: Item
instance of: scholarly article
title: A note on linear extensions and incomparable pairs
zbMATH Open document ID: 0731.06005
DOI: 10.1016/0097-3165(91)90038-I
author: Peter Fishburn
published in: Journal of Combinatorial Theory. Series A
publication date: 1991-01-01T00:00:00Z
review text: For \(2\leq m\leq n\), let P(m,n) denote the family of (strictly) ordered sets on \(\{\) 1,2,...,n\(\}\) in which \(\{\) 1,...,m\(\}\) is an antichain. A characterization is then provided of those members of P(m,n) that maximize the proportion of linear extensions in which 1 lies above 2. The final section of the paper indicates that this suggests a whole class of problems relating to linear extensions and antichains. For example, one could ask to identify those ordered sets in P(m,n) that maximize the proportion of all linear extensions in which \(1>^*2>^*...>^*m\).
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 06A05
zbMATH DE Number: 4208126
zbMATH Keywords: antichain
zbMATH Keywords: linear extensions
reviewed by: Melvin F. Janowitz
MaRDI profile type: Publication
cites work: A correlational inequality for linear extensions of a poset
cites work: Balancing poset extensions
cites work: The XYZ conjecture and the FKG inequality
cites work: Q3731641
full work available at URL: 0097-3165(91)90038-i
OpenAlex ID: W2006819114
description: scientific article; zbMATH DE number 4208126