### 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 |
---|---|

Pages (from-to) | 47-56 |

Number of pages | 10 |

Journal | Combinatorics Probability and Computing |

Volume | 7 |

Issue number | 1 |

Publication status | Published - 1998 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Statistics and Probability
- Theoretical Computer Science

### Cite this

*Combinatorics Probability and Computing*,

*7*(1), 47-56.

**Uniform Intersecting Families with Covering Number Restrictions.** / Frankl, P.; Ota, Katsuhiro; Tokushige, N.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 7, no. 1, pp. 47-56.

}

TY - JOUR

T1 - Uniform Intersecting Families with Covering Number Restrictions

AU - Frankl, P.

AU - Ota, Katsuhiro

AU - Tokushige, N.

PY - 1998

Y1 - 1998

N2 - It is known that any k-uniform family with covering number t has at most kt t-covers. In this paper, we deal with intersecting families and give better upper bounds for the number of t-covers. Let pt(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, pt(k) ≤ kt - 1/√2 ⌊t-1/2⌋3/2kt-1 + O(kt-2). In the cases of t = 4 and 5, we also prove that the coefficient of kt-1 in pt(k) is exactly (t 2).

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

UR - http://www.scopus.com/inward/record.url?scp=0032326585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032326585&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032326585

VL - 7

SP - 47

EP - 56

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 1

ER -