Mandatory representation designs
type: Item
instance of: scholarly article
title: Mandatory representation designs
zbMATH Open document ID: 0661.05014
DOI: 10.1016/0097-3165(88)90061-1
author: Eric Mendelsohn
author: R. S. Rees
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: A pairwise balanced design (PBD) is made up of a set of points X and a collection of subsets B of X such that any pair of distinct points occurs in a unique block. A PBD (K;\(\nu)\) is a pairwise balanced design on \(\nu\) points such that the size of each block is an element of K. A mandatory representation design MR (K;\(\nu)\) is a PBD (K;\(\nu)\) such that for each k in K there is a block in the design whose size is k. In this paper the authors consider the existence of MR (K;\(\nu)\)'s when \(3\in K\). A complete spectrum for MR (3,k;\(\nu)\), k an odd integer, is determined. It is pointed out that MR (3,k;\(\nu)\), k being even, is still an open problem.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4079437
zbMATH Keywords: pairwise balanced design
zbMATH Keywords: PBD
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90061-1
OpenAlex ID: W1993308836
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description: scientific article; zbMATH DE number 4079437