Percentages in pairwise balanced designs

✍ Scribed by Charles J. Colbourn; Vojtech Rődl

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 385 KB
• Volume: 77
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(89)90351-8

✦ Synopsis

Let K = {k,, , k,} be a set of block sizes, and let (pr,

, p,} be nonnegative numbers with Cy!',,p, = 1. We prove the following theorem:

for any E >O, if a (u, K, 1) pairwise balanced design exists and v is sufficiently large, then a (u, K, 1) pairwise balanced design exists in which the fraction of pairs appearing in blocks of size ki is pi f E 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.