Asymptotic enumeration of two-dimensional posets
type: Item
instance of: scholarly article
title: Asymptotic enumeration of two-dimensional posets
zbMATH Open document ID: 0676.06004
DOI: 10.1007/BF00354891
published in: Order
publication date: 1988-01-01T00:00:00Z
review text: It is shown that the number of pairwise nonisomorphic two-dimensional posets with n elements is asymptotically equivalent to \(1/2\;n!\) The estimate is based on the following theorem: For prime two-dimensional posets P there exists a unique unordered pair \(\{L_ 1,L_ 2\}\) of linear extensions of P whose intersection is P. Here a poset P is called prime if there is no subset A of P with the following properties: \(1<| A| <| P|\), for every \(a_ 1,a_ 2\in A\), \(b\in P- A\), \(b<a_ 1\) iff \(b<a_ 2\), \(a_ 1<b\) iff \(a_ 2<b\).
reviewed by: Konrad Engel
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 4106914
zbMATH Keywords: asymptotic enumeration
zbMATH Keywords: symmetric group
zbMATH Keywords: two-dimensional posets
zbMATH Keywords: linear extensions
author: Mohamed H. El-Zahar
author: Norbert Sauer
MaRDI profile type: Publication
cites work: Partial orders of dimension 2
cites work: Partially Ordered Sets
cites work: Asymptotic Enumeration of Partial Orders on a Finite Set
cites work: Q3683903
cites work: Enumeration of Posets Generated by Disjoint Unions and Ordinal Sums
cites work: The Complexity of the Partial Order Dimension Problem
full work available at URL: https://doi.org/10.1007/bf00354891
OpenAlex ID: W2088992086
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description: scientific article; zbMATH DE number 4106914