Every finite distributive lattice is a set of stable matchings
type: Item
instance of: scholarly article
title: Every finite distributive lattice is a set of stable matchings
zbMATH Open document ID: 0546.06009
DOI: 10.1016/0097-3165(84)90056-6
author: N. E. Zubov
published in: Journal of Combinatorial Theory. Series A
publication date: 1984-01-01T00:00:00Z
review text: Each of 2n people, n men and n women, has a linear preference ordering on those of the opposite sex. A matching, i.e. forming n couples, is called stable if one cannot find a woman in one couple and a man in another who would prefer each other to their present partners. The set of stable matchings forms a distributive lattice by defining a partial ordering as follows: one matching is \(\geq\) another if every man is at least as happy with his partner in the first matching as in the second. In this note the author shows that each finite distributive lattice can be represented by a set of stable matchings.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 3869398
zbMATH Keywords: preference ordering
zbMATH Keywords: stable matchings
zbMATH Keywords: finite distributive lattice
reviewed by: Michael Hager
MaRDI profile type: Publication
full work available at URL: 0097-3165(84)90056-6
OpenAlex ID: W2001980959
cites work: College Admissions and the Stability of Marriage
cites work: The Economics of Matching: Stability and Incentives
description: scientific article; zbMATH DE number 3869398