Percentages in pairwise balanced designs

Charles J. Colbourn, Vojtech Rodl

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Let K = {k1,...,km} be a set of block sizes, and let {p1,...,pm} be nonnegative numbers with σmi=1pi = 1. We prove the following theorem: for any ε{lunate} > 0, if a (v,K,1) pairwise balanced design exists and v is sufficiently large, then a (v,K,1) pairwise balanced design exists in which the fraction of pairs appearing in blocks of size ki is pi±ε{lunate} for every i. We also show that the necessary conditions for a pairwise balanced design having precisely the fraction pi of its pairs in blocks of size ki for each i are asymptotically sufficient.

Original languageEnglish (US)
Pages (from-to)57-63
Number of pages7
JournalDiscrete Mathematics
Volume77
Issue number1-3
DOIs
StatePublished - Jan 1 1989
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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