Finite three-dimensional partial orders which are not sphere orders
type: Item
instance of: scholarly article
title: Finite three-dimensional partial orders which are not sphere orders
zbMATH Open document ID: 0941.06005
DOI: 10.1016/S0012-365X(98)00314-8
author: Stefan Felsner
author: Peter Fishburn
author: William T. Trotter
published in: Discrete Mathematics
publication date: 2000-07-27T00:00:00Z
review text: A partially ordered set \(P\) is called a sphere order if there is some \(d\geq 1\) and a function \(F\) which assigns to each \(p\in P\) a sphere in \(\mathbb{R}^d\) such that \(p\leq q\) in \(P\) iff \(F(p) \subseteqq F(q)\). It is shown that there is an integer \(n_0\) so that if \(n\geq n_0\) the direct product of 3 copies of the chain \(0< 1<\dots< n-1\) is not a sphere order. In the proof the authors use a new extension of the product Ramsey theorem.
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 1334541
zbMATH Keywords: circle order
zbMATH Keywords: inclusion representation
zbMATH Keywords: dimension
zbMATH Keywords: partially ordered set
zbMATH Keywords: sphere order
zbMATH Keywords: product Ramsey theorem
reviewed by: Konrad Engel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1334541