### Abstract

Let f_{ r}(n, k) denote the maximum number of k-subsets of an n-set satisfying the condition in the title. It is proved that {Mathematical expression} whenever d=0, 1 or d≦r/2 t^{ 2} with equality holding iff there exists a Steiner system S(t, r(t-1)+1, n-d). The determination of f_{ r}(n, 2 r) led us to a new generalization of BIBD (Definition 2.4). Exponential lower and upper bounds are obtained for the case if we do not put size restrictions on the members of the family.

Original language | English |
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Pages (from-to) | 79-89 |

Number of pages | 11 |

Journal | Israel Journal of Mathematics |

Volume | 51 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Dec 1985 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Israel Journal of Mathematics*,

*51*(1-2), 79-89. https://doi.org/10.1007/BF02772959

**Families of finite sets in which no set is covered by the union of r others.** / Erdős, P.; Frankl, P.; Füredi, Z.

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 51, no. 1-2, pp. 79-89. https://doi.org/10.1007/BF02772959

}

TY - JOUR

T1 - Families of finite sets in which no set is covered by the union of r others

AU - Erdős, P.

AU - Frankl, P.

AU - Füredi, Z.

PY - 1985/12

Y1 - 1985/12

N2 - Let f r(n, k) denote the maximum number of k-subsets of an n-set satisfying the condition in the title. It is proved that {Mathematical expression} whenever d=0, 1 or d≦r/2 t 2 with equality holding iff there exists a Steiner system S(t, r(t-1)+1, n-d). The determination of f r(n, 2 r) led us to a new generalization of BIBD (Definition 2.4). Exponential lower and upper bounds are obtained for the case if we do not put size restrictions on the members of the family.

AB - Let f r(n, k) denote the maximum number of k-subsets of an n-set satisfying the condition in the title. It is proved that {Mathematical expression} whenever d=0, 1 or d≦r/2 t 2 with equality holding iff there exists a Steiner system S(t, r(t-1)+1, n-d). The determination of f r(n, 2 r) led us to a new generalization of BIBD (Definition 2.4). Exponential lower and upper bounds are obtained for the case if we do not put size restrictions on the members of the family.

UR - http://www.scopus.com/inward/record.url?scp=51249175955&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249175955&partnerID=8YFLogxK

U2 - 10.1007/BF02772959

DO - 10.1007/BF02772959

M3 - Article

AN - SCOPUS:51249175955

VL - 51

SP - 79

EP - 89

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1-2

ER -