Small group divisible Steiner quadruple systems
type: Item
instance of: scholarly article
title: Small group divisible Steiner quadruple systems
zbMATH Open document ID: 1179.05019
author: Artem A. Zhuravlev
author: Melissa S. Keranen
author: Donald L. Kreher
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/117230
full work available at URL: v15i1r40.html
review text: Summary: A group divisible Steiner quadruple system, is a triple \((X, {\mathcal H}, {\mathcal B})\) where \(X\) is a \(v\)-element set of points, \({\mathcal H} = \{H_1,H_2,\dots,H_r\}\) is a partition of \(X\) into holes and \({\mathcal B}\) is a collection of 4-element subsets of \(X\) called blocks such that every 3-element subset is either in a block or a hole but not both. In this article we investigate the existence and non-existence of these designs. We settle all parameter situations on at most 24 points, with 6 exceptions. A uniform group divisible Steiner quadruple system is a system in which all the holes have equal size. These were called by Mills G-designs and their existence is completely settled in this article.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 5540945
zbMATH Keywords: group divisible Steiner quadruple system
zbMATH Keywords: Mills G designs
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5540945