Families of finite sets in which no set is covered by the union of r others

P. Erdös, P. Frankl, Z. Füredi

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Let f r(n, k) denote the maximum number of k-subsets of an n-set satisfying the condition in the title. It is proved that {Mathematical expression} whenever d=0, 1 or d≦r/2 t 2 with equality holding iff there exists a Steiner system S(t, r(t-1)+1, n-d). The determination of f r(n, 2 r) led us to a new generalization of BIBD (Definition 2.4). Exponential lower and upper bounds are obtained for the case if we do not put size restrictions on the members of the family.

Original languageEnglish
Pages (from-to)79-89
Number of pages11
JournalIsrael Journal of Mathematics
Issue number1-2
Publication statusPublished - Dec 1 1985


ASJC Scopus subject areas

  • Mathematics(all)

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