The existence of resolvable Steiner quadruple systems

Alan Hartman

doi:10.1016/0097-3165(87)90028-8

The existence of resolvable Steiner quadruple systems

Research output: Contribution to journal › Article › peer-review

Abstract

A Steiner quadruple system of order v is a set X of cardinality v, 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 v≡4 or 8 (mod 12). In this paper we show that this condition is also sufficient for all values of v, with 24 possible exceptions.

Original language	English
Pages (from-to)	182-206
Number of pages	25
Journal	Journal of Combinatorial Theory - Series A
Volume	44
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(87)90028-8
State	Published - Mar 1987
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0097-3165(87)90028-8

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AB - A Steiner quadruple system of order v is a set X of cardinality v, 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 v≡4 or 8 (mod 12). In this paper we show that this condition is also sufficient for all values of v, with 24 possible exceptions.

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The existence of resolvable Steiner quadruple systems

Abstract

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