Angle orders
type: Item
instance of: scholarly article
title: Angle orders
zbMATH Open document ID: 0558.06003
DOI: 10.1007/BF00582739
author: Peter Fishburn
author: William T. Trotter
published in: Order
publication date: 1985-01-01T00:00:00Z
review text: A finite poset is an angle order if its points can be mapped into angular regions in the plane so that x precedes y in the poset precisely when the region for x is properly included in the region for y. Main results: 1. Every poset with dimension 4 or less is an angle order. 2. Every interval order is an angle order. 3. The fact that some angle orders must have an angular region less than 180\(\circ\) (or more than 180\(\circ)\) implies the existence of posets that are not angle orders. Finally, the authors discuss questions about the smallest poset that is not an angle order and other problems, including whether there are dimension 5 posets that are not angle orders.
reviewed by: Bohumil František Šmarda
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 3889591
zbMATH Keywords: angular regions in the plane
zbMATH Keywords: angle orders
zbMATH Keywords: posets
zbMATH Keywords: dimension 5 posets
MaRDI profile type: Publication
cites work: A bound on the dimension of interval orders
cites work: Partially Ordered Sets
cites work: Q5759552
cites work: Interval graphs and interval orders
cites work: On the Dimension of Partially Ordered Sets
cites work: On the complexity of posets
cites work: A Simple Proof of a Theorem of Erdös and Szekeres*
full work available at URL: https://doi.org/10.1007/bf00582739
OpenAlex ID: W4249274350
description: scientific article; zbMATH DE number 3889591