### Abstract

Let K ={K_{1},…, k_{m}} be a set of block sizes, and let {p_{1},…, p_{m}} be nonnegative numbers with Σ^{m}_{i=1}, p_{i} We prove the following theorem: for any ε>0, if a (v, K, 1) pairwise balanced design exists and v is sufficiently large, then a (v, K, 1) pairwise balanced design exists in which the fraction of pairs appearing in blocks of size k_{i}is p_{i},±ε for every i. We also show that the necessary conditions for a pairwise balanced design having precisely the fraction p_{i}, of its pairs in blocks of size k_{i} for each i are asymptotically sufficient.

Original language | English (US) |
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Pages (from-to) | 57-63 |

Number of pages | 7 |

Journal | Annals of Discrete Mathematics |

Volume | 42 |

Issue number | C |

DOIs | |

State | Published - Jan 1 1989 |

Externally published | Yes |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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## Cite this

Colbourn, C. J., & Rötdl, V. (1989). Percentages in Pairwise Balanced Designs.

*Annals of Discrete Mathematics*,*42*(C), 57-63. https://doi.org/10.1016/S0167-5060(08)70097-9