## Abstract

Let X be a finite set of cardinality v. We denote the set of all k-subsets of X by In this paper we consider the problem of partitioning into two parts of equal size, each of which is the block set of a 2-(v k, λ) design. We determine necessary and sufficient conditions on v for the existence of such a partition when k=3 or 4. We also construct partitions for higher values of fc and infinitely many values of v. The case where k=3 has been solved for all values of v by Dehon [5]. The case where v=2k has been solved for all values of k by Alltop [1], The remaining results are new. The technique used is similar to that used by Denniston in his construction of a 4-(12,5,4) design without repeated blocks. We also prove an interesting corollary to Baranyai's theorem giving necessary and sufficient conditions for the existence of a partition of into 1- (v, k,λ) designs.

Original language | English |
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Pages (from-to) | 207-224 |

Number of pages | 18 |

Journal | North-Holland Mathematics Studies |

Volume | 149 |

Issue number | C |

DOIs | |

State | Published - Jan 1987 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics