Linear extensions of finite posets and a conjecture of G. Kreweras on permutations
type: Item
instance of: scholarly article
title: Linear extensions of finite posets and a conjecture of G. Kreweras on permutations
zbMATH Open document ID: 0546.05003
DOI: 10.1016/0012-365X(84)90108-0
author: Gwihen Etienne
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let x be a permutation of \([n]=\{1,2,...,n\}\), n an integer \(\geq 2\). The signature of x is the (n-1)-tuple \(\epsilon =\{\epsilon_ 1,\epsilon_ 2,...,\epsilon_{n-1}\}\) where \(\epsilon_ i\) is the sign \(''+''\) if \(x_ i<x_{i+1}\) and ''-'' otherwise. Let \(P_{\epsilon}\) be the set of permutations of [n] with given signature \(\epsilon\). It is proved that the number of solutions \((x,y)\in P_{\epsilon}\times P_{\epsilon}\) of the equation \(xy=z\) for \(z\in P_{\epsilon}\) does not depend on z in \(P_{\epsilon}\).
reviewed by: Philippe Vincke
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 3869332
zbMATH Keywords: signature
zbMATH Keywords: set of permutations
zbMATH Keywords: linear extension
zbMATH Keywords: finite poset
MaRDI profile type: Publication
Wikidata QID: Q123189867
cites work: Q3910571
cites work: Q3333046
cites work: Ordered structures and partitions
full work available at URL: 0012-365x(84)90108-0
OpenAlex ID: W2027275704
description: scientific article; zbMATH DE number 3869332