Balanced tournament designs with almost orthogonal resolutions. (English) Zbl 0739.05018

Lamken, E. R.; Vanstone, S. A.

J. Aust. Math. Soc., Ser. A 49, No. 2, 175-195 (1990).

Summary: A balanced tournament design, \(BTD(n)\), defined on a \(2n\)-set \(V\) is an arrangement of the \({2n\choose 2}\) distinct unordered pairs of the elements of \(V\) into an \(n\times 2n-1\) 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. 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.

MSC:

05B30

Other designs, configurations

Keywords:

balanced tournament design; orthogonal resolutions