The existence of resolvable Steiner quadruple systems
type: Item
instance of: scholarly article
title: The existence of resolvable Steiner quadruple systems
zbMATH Open document ID: 0663.05010
DOI: 10.1016/0097-3165(87)90028-8
author: Alan Hartman
published in: Journal of Combinatorial Theory. Series A
publication date: 1987-01-01T00:00:00Z
review text: A Steiner quadruple system of order \(\nu\) is a set X of cardinality \(\nu\), and a set Q, of 4-subsets of X, called blocks, with the property that every 3-subset of X is contained in a unique block. A Steiner quadruple system is resolvable if Q can be partitioned into parallel classes (partitions of X). A necessary condition for the existence of a resolvable Steiner quadruple system is that \(\nu\) \(\equiv 4\) or 8 (mod 12). In this paper we show that this condition is also sufficient for all values of \(\nu\), with 24 possible exceptions.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 4083635
zbMATH Keywords: Steiner quadruple system
zbMATH Keywords: parallel classes
zbMATH Keywords: partitions
MaRDI profile type: Publication
full work available at URL: 0097-3165(87)90028-8
OpenAlex ID: W2082134848
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description: scientific article; zbMATH DE number 4083635