J Austral Math Soc Ser A 49 pp175--195, 1990.

Balanced Tournament Designs with almost Orthogonal Resolutions

E. R. Lamken and S. A. Vanstone

Abstract

A balanced tournament design, BTD(n), defined on a 2n-set V is an arrangement of the ²ⁿC₂ distinct unordered pairs of the elements of V into an n ×2n - 1 array such that (1) every element of V is contained in precisely one cell of each column, and (2) every element of V is contained in at most two cells of each row. In this paper, we investigate the existence of balanced tournament designs with a pair of almost orthogonal resolutions. These designs can be used to construct doubly resolvable (v, 3, 2)-BIBDs and, in our smallest applications, have been used to construct previously unknown doubly resolvable (v, 3, 2)-BIBDs.

1980 AMS Subject Classification (1985 Revision): 05B30

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Authors

E. R. Lamken

S. A. Vanstone

Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.