## 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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