On finite matroids with one more hyperplane than points
type: Item
instance of: scholarly article
title: On finite matroids with one more hyperplane than points
zbMATH Open document ID: 0847.05032
DOI: 10.1007/BF01223034
author: Eva Ferrara Dentice
published in: Journal of Geometry
publication date: 1996-09-29T00:00:00Z
review text: Let \(n\) be a natural number \(\geq 2\). An \(n\)-dimensional Bridges space is a finite \(n\)-dimensional linear space in which there are \(b_{n+1} = \nu + 1\) hyperplanes, where \(\nu\) is the number of points. The main result of the paper is the following theorem: An \(n\)-dimensional Bridges space \(L\) with \(n \geq 3\) has one of the following structures: (i) an \(n\)-dimensional Galois projective space with one point deleted; (ii) the direct sum of a generalized projective space and a \(t\)-dimensional Bridges space, for a suitable \(t \leq n - 1\). This result extends the classification of 2-dimensional and 3-dimensional Bridges spaces to a general \(n\).
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 872716
zbMATH Keywords: finite matroids
zbMATH Keywords: Bridges space
zbMATH Keywords: hyperplanes
zbMATH Keywords: Galois projective space
zbMATH Keywords: classification
reviewed by: Mirela Ştefănescu
MaRDI profile type: Publication
cites work: Q5575259
cites work: Near 1-designs
cites work: Diagrams for geometries and groups
cites work: On Representatives of Subsets
cites work: On an application of Hall's representatives theorem to a finite geometry problem
cites work: Q4028445
description: scientific article; zbMATH DE number 872716