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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 281.04002

**Autor: ** Erdös, Paul; Kleitman, Daniel J.

**Title: ** Extremal problems among subsets of a set. (In English)

**Source: ** Discrete Math. 8, 281-294 (1974).

**Review: ** This paper is a review of results and progress in the study of extremal problems on collection of subsets of a finite set, as of the spring of 1970, as presented at the 1970 Chapel Hill Conference. A typical problem might be given a collection of subsets of an n element set such that no two members have exactly k or fewer elements in common, how large can the collection be? Much has been accomplished in this area since 1970. A more recent review is contained in the article by *G.O.H.Katona* in Combinatorics, Part 2 , Proc. Adv. Stud. Inst., Breukelen, 13-42 (1974; Zbl 298.05142) on Extremal problems for hypergraphs; a paper by *C. Greene* and *D.J.Kleitman* in MAA Studies in Mathematics 17, Stud. in Combinatorics 22-79 (1978; Zbl 409.05012) reviews some of the methods that have been developed for such problems.

**Classif.: ** * 04A20 Combinatorial set theory

05A05 Combinatorial choice problems

04-02 Research monographs (set theory)

05-02 Research monographs (combinatorics)

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