### Abstract

Let X be a finite set of n-melements and suppose t ≥ 0 is an integer. In 1975, P. Erdös asked for the determination of the maximum number of sets in a family F = {F_{1},..., F_{m}}, F_{i} ⊂ X, such that ∥F_{i} ∩ F_{j}∥ ≠ t for 1 ≤ i ≠ j ≤ m. This problem is solved for n ≥ n_{0}(t). Let us mention that the case t = 0 is trivial, the answer being 2^{n - 1}. For t = 1 the problem was solved in [3]. For the proof a result of independent interest (Theorem 1.5) is used, which exhibits connections between linear algebra and extremal set theory.

Original language | English |
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Pages (from-to) | 230-236 |

Number of pages | 7 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 36 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 1984 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics