A geometric condition for incidence-matrix nullvectors
type: Item
instance of: scholarly article
title: A geometric condition for incidence-matrix nullvectors
zbMATH Open document ID: 0678.05011
DOI: 10.1016/0097-3165(89)90085-X
author: Stephen D. Smith
published in: Journal of Combinatorial Theory. Series A
publication date: 1989-01-01T00:00:00Z
review text: Let (P,L) be a (point,line)-geometry, in which L is a collection of subsets of size \(s+1\) of P. Suppose there exists a function e: \(P\to {\mathbb{Z}}\) such that, for each \(p\in P\) and \(\ell \in L\), there is a unique \(q\in \ell\) such that \(e(\ell)=\{e(q),e(q)+1\}\). Then \(\sum_{p\in P}(- s)^{-e(p)}P\) lies in the kernel of the point-line incidence matrix of (P,L). Several instances of this phenomenon (notably) near polygons and an infinite cover) are discussed.
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 4110704
zbMATH Keywords: incidence systems
zbMATH Keywords: finite geometry
zbMATH Keywords: near polygons
reviewed by: Arjeh M. Cohen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4110704