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 |
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Pages (from-to) | 182-206 |
Number of pages | 25 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 44 |
Issue number | 2 |
DOIs | |
State | Published - Mar 1987 |
Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics