Orbits of infinite block designs
type: Item
instance of: scholarly article
title: Orbits of infinite block designs
zbMATH Open document ID: 0878.05010
DOI: 10.1016/S0012-365X(96)00112-4
author: B. S. Webb
published in: Discrete Mathematics
publication date: 1997-06-16T00:00:00Z
review text: This article investigates automorphism groups of simple balanced incomplete block designs with \(v\) infinite and \(k\) finite. If such a group has \(N\) block and \(n\) point orbits then it is possible to have \(N<n\). The author gives bounds for these numbers showing, in particular, that \(N\geq n\) provided \(n\geq k(k-1)\). For the case \(k=3\) this is strengthened to \(N\geq n\) without restriction. The author also investigates block-transitive designs, giving bounds for the point-rank which are known in the case that the group is also point-transitive.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1021700
zbMATH Keywords: automorphism group
zbMATH Keywords: simple balanced incomplete block designs
zbMATH Keywords: block-transitive designs
MaRDI profile type: Publication
cites work: On the orbits of collineation groups
cites work: Remarques sur l'homogeneite des espaces linéaires et des systèmes de blocs
cites work: An orbit theorem for Steiner triple systems
cites work: Automorphism groups of block designs which are block transitive
cites work: A new strongly minimal set
full work available at URL: s0012-365x(96)00112-4
OpenAlex ID: W2040252477
description: scientific article; zbMATH DE number 1021700