### Abstract

A disjoint system of type (∀, ∃, k, n) is a collection 풞 = {풜_{1},…, 풜_{m}} of pairwise disjoint families of k‐subsets of an n‐element set satisfying the following condition. For every ordered pair 풜_{i} and 풜_{j} of distinct members of 풞 and for every A ϵ 풜_{i} there exists a B ϵ 풜_{j} that does not intersect A. Let D_{n} (∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k ⩾ 2,. (Formula Presented.) This settles a problem of Ahlswede, Cai, and Zhang. Several related problems are considered as well.

Original language | English (US) |
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Pages (from-to) | 13-20 |

Number of pages | 8 |

Journal | Random Structures & Algorithms |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1995 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)
- Computer Graphics and Computer-Aided Design
- Applied Mathematics

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## Cite this

Alon, N., & Sudakov, B. (1995). Disjoint systems.

*Random Structures & Algorithms*,*6*(1), 13-20. https://doi.org/10.1002/rsa.3240060103