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

Access to Document

10.1016/0097-3165(87)90028-8

Cite this

@article{590b1dd3e2ce41b18ee235931fafded2,

title = "The existence of resolvable Steiner quadruple systems",

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.",

author = "Alan Hartman",

year = "1987",

month = mar,

doi = "10.1016/0097-3165(87)90028-8",

language = "English",

volume = "44",

pages = "182--206",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - The existence of resolvable Steiner quadruple systems

AU - Hartman, Alan

PY - 1987/3

Y1 - 1987/3

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=38249034925&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(87)90028-8

DO - 10.1016/0097-3165(87)90028-8

M3 - Article

AN - SCOPUS:38249034925

SN - 0097-3165

VL - 44

SP - 182

EP - 206

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 2

ER -

The existence of resolvable Steiner quadruple systems

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this