On an application of Hall's representatives theorem to a finite geometry problem
type: Item
instance of: scholarly article
title: On an application of Hall's representatives theorem to a finite geometry problem
zbMATH Open document ID: 0659.05032
DOI: 10.1007/BF01848058
author: Zbigniew Romanowicz
author: Krzysztof Kołodziejczyk
published in: Periodica Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: The authors consider finite planar spaces, i.e. finite linear spaces together with a family of subspaces (``planes'') such that each non- collinear triple of points determines exactly one plane. They provide an elementary proof for the fact that the number of planes is at least as large as the number of points; they also describe the possible structure of planar spaces achieving equality. These results are derived by using P. Hall's marriage theorem. As the authors point out, similar results have been obtained in terms of lattice and matroid theory previously.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 4077238
zbMATH Keywords: finite geometries
zbMATH Keywords: Hall's theorem
zbMATH Keywords: planar spaces
zbMATH Keywords: linear spaces
MaRDI profile type: Publication
cites work: Q5575259
cites work: Finite linear spaces and projective planes
cites work: On Representatives of Subsets
cites work: A property of the hyperplanes of a matroid and an extension of Dilworth's theorem
cites work: Q3310509
full work available at URL: https://doi.org/10.1007/bf01848058
OpenAlex ID: W2023935760
description: scientific article; zbMATH DE number 4077238