All directed BIBDs with k = 3 exist期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

All directed BIBDs with k = 3 exist

Authors:	Jennifer Seberry David Skillicorn

Affiliation:	Department of Applied Mathematics, University of Sydney N.S.W., Australia;Department of Computer Science, University of Manitoba Winnipeg, Canada

Abstract:	A directed BIBD with parameters ( $υ, b, r, k, λ^{1}$ ) is a BIBD with parameters ( $υ, b, r, k, 2λ^{1}$ ) in which each ordered pair of varieties occurs together in exactly $λ^{1}$ blocks. It is shown that $λ^{1} υ(υ ? 1) ≡ 0$ (mod 3) is a necessary and sufficient condition for the existence of a directed ( $υ, b, r, k, λ^{1}$ ) BIBD with k = 3.

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