Regular Article
Intersecting Balanced Families of Sets

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Abstract

Suppose that any t members (t⩾2) of a regular family on an n element set have at least k common elements. It is proved that the largest member of the family has at least k1/tn1−1/t elements. The same holds for balanced families, which is a generalization of the regularity. The estimate is asymptotically sharp.

Keywords

extremal problems
regular family
balanced family

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Communicated by the Managing Editors

f1

E-mail: [email protected]

f2

E-mail: [email protected]

f3

E-mail: [email protected]

1

The work of the second author was supported by the Hungarian National Foundation for Scientific Research Grant T029255 and the UNESCO Venice Office ROSTE, Grant 875.630.9.