### Abstract

A disjoint system of type (∀, ∃, k, n) is a collection C={A_{1}, …, A_{m}} of pairwise disjoint families of k-subsets of an n-element set satisfying the following condition. For every ordered pair A_{i} and A_{j} of distinct members of C and for every A ∈ A_{i} there exists a B ∈ A_{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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Title of host publication | Algebraic Coding - 1st French-Israeli Workshop, Proceedings |

Publisher | Springer Verlag |

Pages | 159-163 |

Number of pages | 5 |

ISBN (Print) | 9783540578437 |

State | Published - Jan 1 1994 |

Externally published | Yes |

Event | 1st French-Israeli Workshop on Algebraic Coding, 1993 - Paris, France Duration: Jul 19 1993 → Jul 21 1993 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 781 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st French-Israeli Workshop on Algebraic Coding, 1993 |
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Country | France |

City | Paris |

Period | 7/19/93 → 7/21/93 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Alon, N. M., & Sudakov, B. (1994). Disjoint systems. In

*Algebraic Coding - 1st French-Israeli Workshop, Proceedings*(pp. 159-163). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 781 LNCS). Springer Verlag.