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**Zentralblatt MATH**

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

**Zbl.No: ** 496.05009

**Autor: ** Erdös, Paul; Faber, Vance; Jones, F.

**Title: ** Projective (2n,n,\lambda,1)-designs. (In English)

**Source: ** J. Stat. Plann. Inference 7, 181-191 (1982).

**Review: ** The paper deals exclusively of \lambda-covers, i.e. of sets S with 2n elements with a system of blocks of n elements such that each point of S is in \lambda blocks and every two blocks have a non-empty intersection. The problem of existence of such covers with given parameters is completely solved in the paper. Interesting results on the existence of subcovers and on extensions of a cover with a not too great \lambda to a (\lambda+2)-cover on the same set are obtained. As conclusion, a set of open problems with some remarks is given. Proofs are mainly by construction, by induction, by cases and by quotations, using graph theory too.

**Reviewer: ** G.Ferrero

**Classif.: ** * 05B05 Block designs (combinatorics)

05B30 Other designs, configurations

05C65 Hypergraphs

05B40 Packing and covering (combinatorics)

**Keywords: ** predesign; subdesign; lambda-covers; subcovers; primitive covers

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