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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

##### MSC:
 05A05 Permutations, words, matrices 05B07 Triple systems 05C65 Hypergraphs
subsets
Full Text:
##### References:
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