### Abstract

Let X be a finite set of n elements and ℱ a family of 4 a+5-element subsets, a≧6. Suppose that all the pairwise intersections of members of ℱ have cardinality 0, a or 2 a+1. We show that c_{ 1} n^{ 4/3} 2 n^{ 4/3} for some positive c_{ i}'s. This answers a question of P. Frankl.

Original language | English |
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Pages (from-to) | 27-31 |

Number of pages | 5 |

Journal | Combinatorica |

Volume | 5 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1985 |

### Fingerprint

### Keywords

- AMS subject classification (1980): 05C35, 05C65

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Combinatorica*,

*5*(1), 27-31. https://doi.org/10.1007/BF02579439

**Set systems with three intersections.** / Füredi, Z.

Research output: Contribution to journal › Article

*Combinatorica*, vol. 5, no. 1, pp. 27-31. https://doi.org/10.1007/BF02579439

}

TY - JOUR

T1 - Set systems with three intersections

AU - Füredi, Z.

PY - 1985/3

Y1 - 1985/3

N2 - Let X be a finite set of n elements and ℱ a family of 4 a+5-element subsets, a≧6. Suppose that all the pairwise intersections of members of ℱ have cardinality 0, a or 2 a+1. We show that c 1 n 4/3 2 n 4/3 for some positive c i's. This answers a question of P. Frankl.

AB - Let X be a finite set of n elements and ℱ a family of 4 a+5-element subsets, a≧6. Suppose that all the pairwise intersections of members of ℱ have cardinality 0, a or 2 a+1. We show that c 1 n 4/3 2 n 4/3 for some positive c i's. This answers a question of P. Frankl.

KW - AMS subject classification (1980): 05C35, 05C65

UR - http://www.scopus.com/inward/record.url?scp=51249175098&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249175098&partnerID=8YFLogxK

U2 - 10.1007/BF02579439

DO - 10.1007/BF02579439

M3 - Article

VL - 5

SP - 27

EP - 31

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 1

ER -