## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  489.05003
Autor:  Erdös, Paul; Frankl, P.; Fueredi, Z.
Title:  Families of finite sets in which no set is covered by the union of two others. (In English)
Source:  J. Comb. Theory, Ser. A 33, 158-166 (1982).
Review:  From the summary: Let f^*(n) denote the maximum of k-subsets of an n-set satisfying the condition in the title. It is proved that f2t-1(n) \leq f2t(n+1) \leq \binom{n}{t}/\binom{2t-1}{t} with equalities holding iff there exists a Steiner system \Cal{S}(t,2t-1,n). The bounds are approximately best possible for k \leq 6 and of correct order of magnitude for k \geq 7, as well, even if the corresponding Steiner systems do not exist.''
Reviewer:  J.Libicher
Classif.:  * 05A05 Combinatorial choice problems
05B07 Triple systems
05C65 Hypergraphs
Keywords:  subsets

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