Interval orders and circle orders
type: Item
instance of: scholarly article
title: Interval orders and circle orders
zbMATH Open document ID: 0663.06003
DOI: 10.1007/BF00354889
published in: Order
publication date: 1988-01-01T00:00:00Z
review text: A finite partially ordered set \((X,<_ 0)\) is said to be an interval order if each \(x\in X\) can be mapped into a bounded closed real interval I(x) so that, for all \(x,y\in X\), \(x<_ 0y\Leftrightarrow \sup I(x)<\inf I(y)\); it is said to be a circle order if each \(x\in X\) can be mapped into a circular disk \(C(x)\subseteq R^ 2\) so that, for all \(x,y\in X\), \(x<_ 0\Leftrightarrow C(x)\subset C(y)\). This paper proves that every finite interval order is a circle order.
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 4083688
zbMATH Keywords: interval order
zbMATH Keywords: circle order
author: Peter Fishburn
reviewed by: Josef Niederle
MaRDI profile type: Publication
cites work: A bound on the dimension of interval orders
cites work: Partially Ordered Sets
cites work: Intransitive indifference with unequal indifference intervals
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cites work: Angle orders, regular n-gon orders and the crossing number
cites work: Circle orders, n-gon orders and the crossing number
cites work: Q3815303
full work available at URL: https://doi.org/10.1007/bf00354889
OpenAlex ID: W2018598735
description: scientific article; zbMATH DE number 4083688