How to construct a partition when preference sets are given
type: Item
instance of: scholarly article
title: How to construct a partition when preference sets are given
zbMATH Open document ID: 0821.90003
DOI: 10.1016/0305-0548(94)90036-1
author: Ely Merzbach
author: Boris Singer
published in: Computers \& Operations Research
publication date: 1995-01-15T00:00:00Z
review text: Let \(E\) and \(I\) be two sets. A preference set family for \(E\) is a family \((A_{ij})_{i,j\in I}\) of subsets of \(E\) such that \(A_{ii}= E\) for every \(i\in I\) and \(A_{ij}= E\backslash A_{ji}\) for every \(i,j\in I\) with \(i\neq j\). The relation \(x\in A_{ij}\) is interpreted as \(x\) prefers \(i\) to \(j\). The main result in the paper states that, if the transitivity property \(A_{ij}\cap A_{jk}\subset A_{ik}\), for every \(i,j,k\in I\) holds, then the family \((\bigcap_{j\in I} A_{ij})_{i\in I}\) is a partition of \(E\).
Mathematics Subject Classification ID: 91B08
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 90C27
zbMATH DE Number: 711787
zbMATH Keywords: partition
zbMATH Keywords: preference sets
zbMATH Keywords: tessellation
zbMATH Keywords: post-office problem
zbMATH Keywords: transitivity property
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: 0305-0548(94)90036-1
OpenAlex ID: W2043483773
cites work: Q4039784
cites work: Q5568975
cites work: Computing Dirichlet Tessellations in the Plane
cites work: Q5508167
cites work: Mediatrix of two arcs of a quasicircle
description: scientific article; zbMATH DE number 711787