### Abstract

Answering a question of Erdös, Sauer [4] and independently Perles and Shelah [5] found the maximal cardinality of a collection F of subsets of a set: N of cardinality n such that for every subset M ⊂ N of cardinality m |{C ∩ M: C ε{lunate} F}| < 2^{m}. Karpovsky and Milman [3] generalised this result. Here we give a short proof of these results and further extensions.

Original language | English (US) |
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Pages (from-to) | 199-202 |

Number of pages | 4 |

Journal | Discrete Mathematics |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - 1983 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Alon, N. (1983). On the density of sets of vectors.

*Discrete Mathematics*,*46*(2), 199-202. https://doi.org/10.1016/0012-365X(83)90253-4