Symmetric designs and geometroids
type: Item
instance of: scholarly article
title: Symmetric designs and geometroids
zbMATH Open document ID: 0682.05015
DOI: 10.1007/BF02122683
author: T. P. McDonough
author: V. C. Mavron
published in: Combinatorica
publication date: 1989-01-01T00:00:00Z
review text: A \(\lambda\)-set in a symmetric 2-(v,k,\(\lambda)\) design \(\Pi\) is a subset S meeting every block in 0, 1 or \(\lambda\) points such that for any point of S there is a unique block meeting S at that point only. In this paper, families of symmetric 2-designs containing \(\lambda\)-sets are investigated. First it is shown that if \(\Pi\) has a \(\lambda\)-set, then it is a geometroid with \(v=\lambda u^ 2+u+1\) and \(k=\lambda u+1\), where \(u\geq \lambda -1\). The particular attention is then payed to the existence of three special families of geometroids with \(\lambda\)-sets, namely the geometroids with \(u=\lambda -1\), \(\lambda\), and \(\lambda +1\). Some open problems are discussed, as well.
reviewed by: J.Libicher
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 51E05
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 4116546
zbMATH Keywords: symmetric design
zbMATH Keywords: geometroid
MaRDI profile type: Publication
cites work: Ovals in projective designs
cites work: The Geometry of Two-Weight Codes
cites work: Q4767325
cites work: Some techniques for constructing infinite families of BIBD's
cites work: Maximal arcs in designs
cites work: Q4085734
full work available at URL: https://doi.org/10.1007/bf02122683
OpenAlex ID: W1964012991
description: scientific article; zbMATH DE number 4116546