### Abstract

It is known that any k-uniform family with covering number t has at most k^{t} t-covers. In this paper, we deal with intersecting families and give better upper bounds for the number of t-covers. Let p_{t}(k) be the maximum number of t-covers in any k-uniform intersecting families with covering number t. We prove that, for a fixed t, p_{t}(k) ≤ k^{t} - 1/√2 ⌊t-1/2⌋^{3/2}k^{t-1} + O(k^{t-2}). In the cases of t = 4 and 5, we also prove that the coefficient of k^{t-1} in p_{t}(k) is exactly (^{t}_{2}).

Original language | English |
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Pages (from-to) | 47-56 |

Number of pages | 10 |

Journal | Combinatorics Probability and Computing |

Volume | 7 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Frankl, P., Ota, K., & Tokushige, N. (1998). Uniform Intersecting Families with Covering Number Restrictions.

*Combinatorics Probability and Computing*,*7*(1), 47-56. https://doi.org/10.1017/S096354839700326X