Linear spaces with a regularity condition
type: Item
instance of: scholarly article
title: Linear spaces with a regularity condition
zbMATH Open document ID: 0781.51004
author: Frederic Nicholson
author: Albrecht Beutelspacher
published in: Ricerche di Matematica
publication date: 1993-01-17T00:00:00Z
review text: A linear space is an incidence structure such that any line contains at least two points and through any two different points exactly one line is passing. In the paper finite linear spaces with the following regularity property are studied: There exist two integers \(s,t\) such that for any two disjoint lines \(p,q\) and point \(P\) outside of them are either \(s\) or \(t\) lines going through \(P\) and intersecting \(p\) and \(q\). The case \(s=t\) was described completely in an earlier common paper of A. Delandtsheer and the second author. For \(s\neq t\) the situation looks more complicated and it is very difficult to classify all such linear spaces. In the paper several properties of linear spaces with regularity \(s\neq t\) are presented and two special classes are described.
Mathematics Subject Classification ID: 51A20
zbMATH DE Number: 96523
zbMATH Keywords: regularity condition
zbMATH Keywords: incidence structure
reviewed by: J. Bureš
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 96523