## Abstract

A Steiner system (X, ß), denoted S_{λ}(t, k, v), is a set X of points, of cardinality v, and a collection β of k-subsets of X called blocks, with the property that every t-subset of X is contained in precisely λ blocks. A quadruple system is a Steiner system S_{1}(3,4, v). A triple (X, β, γ) is called an (s, μ)-resolvable system if, for some s<t, it is a partition of an S_{λ}(t, k, v) system (X, β) into subsystems (X, γ_{1}), each of which is an S_{μ} (s, k, v) system, such that γ=γ_{1}|γ_{2}|…|γ_{c} is a partition of β. A system is doubly resolvable if it is resolvable and each (X, γ_{1}) is also resolvable. This article surveys the work done on the existence of (s, μ)-resolvable and doubly-resolvable quadruple systems for (s, μ)=(2, 1), (2, 3) and (1, 1).

Original language | English |
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Pages (from-to) | 143-150 |

Number of pages | 8 |

Journal | Annals of Discrete Mathematics |

Volume | 7 |

Issue number | C |

DOIs | |

State | Published - 1 Jan 1980 |

Externally published | Yes |

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics