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On near generalized balanced tournament designs

โœ Scribed by E.R. Lamken

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
941 KB
Volume
97
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Lamken, E.R., On near generalized balanced tournament designs, Discrete Mathematics 97 (1991) 279-294. A near generalized balanced tournament design, NGBTD(n, k), defined on a (kn + l)-set V, is an arrangement of the blocks of a (kn + 1, k, k -I)-BIBD defined on V into an n x (kn + 1) array so that (1) every element of V occurs precisely k times in each row, (2) every column of the array contains kn distinct elements of V, and (3) the columns form a near resolution of the (kn + 1, k, kl)-BIBD.

It is easy to construct NGBTD(n, 2) for n a positive integer. In this paper, we investigate the existence of NGBTD(n, k)s for k 2 3. We describe direct and recursive constructions for NGBTD(n, k)s. One of our main results is to show that there exists a NGBTD(n, 3) for n a positive integer except possibly for n E (3, 38, 39, 118).

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