Percentages in Pairwise Balanced Designs

Charles Colbourn, Vojtech Rötdl

Research output: Contribution to journalArticle

Abstract

Let K ={K1,..., km } be a set of block sizes, and let {p1,..., pm} be nonnegative numbers with Σm i=1, pi We prove the following theorem: for any ε>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 kiis pi,±ε 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
JournalAnnals of Discrete Mathematics
Volume42
Issue numberC
DOIs
StatePublished - 1989
Externally publishedYes

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Pairwise Balanced Design
Pi
Percentage
p.m.
Non-negative
Sufficient
Necessary Conditions
Theorem

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Percentages in Pairwise Balanced Designs. / Colbourn, Charles; Rötdl, Vojtech.

In: Annals of Discrete Mathematics, Vol. 42, No. C, 1989, p. 57-63.

Research output: Contribution to journalArticle

Colbourn, Charles ; Rötdl, Vojtech. / Percentages in Pairwise Balanced Designs. In: Annals of Discrete Mathematics. 1989 ; Vol. 42, No. C. pp. 57-63.
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