The existence of resolvable Steiner quadruple systems

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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 languageEnglish
Pages (from-to)182-206
Number of pages25
JournalJournal of Combinatorial Theory - Series A
Issue number2
StatePublished - Mar 1987
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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