On circle containment orders
type: Item
instance of: scholarly article
title: On circle containment orders
zbMATH Open document ID: 0667.06002
DOI: 10.1007/BF00714474
author: Edward Scheinerman
author: John C. Wierman
published in: Order
publication date: 1988-01-01T00:00:00Z
review text: A partially ordered set is called a circle containment order provided it is isomorphic to a poset of circles in the plane ordered by inclusion. In this paper it is shown that the infinite three-dimensional poset \({\mathcal Z}^ 3\) is not a circle containment order. This fact contrasts with the conjecture that every finite three-dimensional poset is a circle order.
reviewed by: Hiroshi Yutani
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 4091570
zbMATH Keywords: circle containment order
zbMATH Keywords: poset
MaRDI profile type: Publication
cites work: Degrees of freedom versus dimension for containment orders
cites work: Partially Ordered Sets
cites work: Angle orders
cites work: Containment Graphs, Posets, and Related Classes of Graphs
cites work: Q5598258
cites work: Angle orders, regular n-gon orders and the crossing number
cites work: Circle orders, n-gon orders and the crossing number
full work available at URL: https://doi.org/10.1007/bf00714474
OpenAlex ID: W1975250653
description: scientific article; zbMATH DE number 4091570