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

P. Erdős, P. Frankl, Z. Füredi

Research output: Contribution to journalArticle

290 Citations (Scopus)

Abstract

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
Volume51
Issue number1-2
DOIs
Publication statusPublished - Dec 1985

Fingerprint

Steiner System
Finite Set
Upper and Lower Bounds
Equality
Union
Denote
Restriction
Subset
Generalization
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Families of finite sets in which no set is covered by the union of r others. / Erdős, P.; Frankl, P.; Füredi, Z.

In: Israel Journal of Mathematics, Vol. 51, No. 1-2, 12.1985, p. 79-89.

Research output: Contribution to journalArticle

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