Abstract
A pairwise balanced design (PBD) of index unity is a pair (X,A) where X is a set (of points) and A a class of subsets A of X (called blocks) such that any pair of distinct points of X is contained in exactly one of the blocks of A (and we may also require |A| ≥ 2 for each A ∈ A). Such systems are also known as linear spaces. PBD’s where all blocks have the same size |A| = k are known as balanced incomplete block designs (BIBD’s) of index λ = 1, as 2 - (v,k,1) designs, and as Steiner systems S(2,k,v). The more general concept, where multiple block sizes are allowed, was introduced by BOSE, Shrikhande & Parker [4] and H. Hanani [9], and played important roles in their respective work on orthogonal Latin squares and Bibd’s.
This research was supported in part by NSF Grant GP-28943 (O.S.U.R.F. Project No. 3228-A1).
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© 1975 Mathematical Centre, Amsterdam
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Wilson, R.M. (1975). Constructions and Uses of Pairwise Balanced Designs. In: Hall, M., van Lint, J.H. (eds) Combinatorics. NATO Advanced Study Institutes Series, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1826-5_2
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DOI: https://doi.org/10.1007/978-94-010-1826-5_2
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