A note on almost partial geometries
type: Item
instance of: scholarly article
title: A note on almost partial geometries
zbMATH Open document ID: 0916.51008
author: P. H. Fisher
published in: European Journal of Combinatorics
publication date: 1999-07-14T00:00:00Z
review text: An almost partial geometry (APG) is a connected incidence structure with \(v\) points and \(b\) lines that satisfy: (1) there are \(k>1\) points on each line; (2) each point is on \(r>1\) lines (two points are on at most 1 line); (3) for each point \(P\) there exists a unique line \(P^\alpha\) with \(P\notin P^\alpha\) such that the number of points on \(P^\alpha\) joint to \(P\) is a constant \(e\) and for any other line \(l\) with \(P\notin l\neq P^\alpha\) the number of points on \(l\) joint to \(P\) is a constant \(t>0\). The APG is called symmetric if \(k=r\). If \(e=t\) then an APG is a partial geometry. We shall call an APG proper if \(e\neq t\). In this paper the following result is proved: A proper APG is symmetric with \(e\) even.
Mathematics Subject Classification ID: 51E14
zbMATH DE Number: 1212315
zbMATH Keywords: partial geometry
reviewed by: Alexandre A. Makhnev
MaRDI profile type: Publication
full work available at URL: eujc.1997.0155
OpenAlex ID: W2044117588
DOI: 10.1006/EUJC.1997.0155
description: scientific article; zbMATH DE number 1212315