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Families of finite sets in which no set is covered by the union of two others. (English) Zbl 0489.05003
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 \(f^{2t-1}(n)\leq f^{2t}(n+1)\leq\binom{n}{t}/\binom{2t-1}{t}\) with equalities holding iff there exists a Steiner system \(\mathcal{S}(t,2t-1,n)\). 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

05A05 Permutations, words, matrices
05B07 Triple systems
05C65 Hypergraphs
Full Text: DOI
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