### Abstract

Let ℬ(n, ≤ 4) denote the subsets of [n]:=\{ 1, 2, \dots, n\} of at most 4 elements. Suppose that ℱ is a set system with the property that every member of ℬ can be written as a union of (at most) two members of ℱ. (Such an ℱ is called a 2-base of ℬ) Here we answer a question of Erdos proving that |ℱ|≥ 1+n+\binom{n}{2}- {4/3n}, and this bound is best possible for n ≥ 8.

Original language | English |
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Pages (from-to) | 131-141 |

Number of pages | 11 |

Journal | Combinatorics Probability and Computing |

Volume | 15 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jan 2006 |

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### ASJC Scopus subject areas

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

### Cite this

*Combinatorics Probability and Computing*,

*15*(1-2), 131-141. https://doi.org/10.1017/S0963548305007248

**2-Bases of quadruples.** / Füredi, Z.; Katona, Gyula O H.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 15, no. 1-2, pp. 131-141. https://doi.org/10.1017/S0963548305007248

}

TY - JOUR

T1 - 2-Bases of quadruples

AU - Füredi, Z.

AU - Katona, Gyula O H

PY - 2006/1

Y1 - 2006/1

N2 - Let ℬ(n, ≤ 4) denote the subsets of [n]:=\{ 1, 2, \dots, n\} of at most 4 elements. Suppose that ℱ is a set system with the property that every member of ℬ can be written as a union of (at most) two members of ℱ. (Such an ℱ is called a 2-base of ℬ) Here we answer a question of Erdos proving that |ℱ|≥ 1+n+\binom{n}{2}- {4/3n}, and this bound is best possible for n ≥ 8.

AB - Let ℬ(n, ≤ 4) denote the subsets of [n]:=\{ 1, 2, \dots, n\} of at most 4 elements. Suppose that ℱ is a set system with the property that every member of ℬ can be written as a union of (at most) two members of ℱ. (Such an ℱ is called a 2-base of ℬ) Here we answer a question of Erdos proving that |ℱ|≥ 1+n+\binom{n}{2}- {4/3n}, and this bound is best possible for n ≥ 8.

UR - http://www.scopus.com/inward/record.url?scp=29744434736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29744434736&partnerID=8YFLogxK

U2 - 10.1017/S0963548305007248

DO - 10.1017/S0963548305007248

M3 - Article

AN - SCOPUS:29744434736

VL - 15

SP - 131

EP - 141

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 1-2

ER -