IJPAM: Volume 54, No. 4 (2009)
TWO ASSOCIATE CLASSES AND




University of the Thai Chamber of Commerce
126/1 Vibhavadee-Rangsit Road, Dindaeng, Bangkok, 10400, THAILAND


Abstract.A group divisible design GDD
is a collection of
-subsets (called blocks)
of a
-set of symbols where: the
-set is divided into
groups; each
pair of symbols from the same group occurs in exactly
blocks; and each
pair symbols from different groups occurs in exactly
blocks. Pairs of symbols occurring in the same group are known to statisticians as first associates, and pairs occurring in different groups are called second associates. The existence of such GDDs has been of interest over the years, going back to at least the work of Bose and Shimamoto in 1952 who began classifying such designs. Recently, such an existence problem when
was solved in the case where the groups have the same size and the blocks have size 3. In this paper, we continue to focus on blocks of size 3, solving the problem when the required designs
having two groups of unequal
sizes and
and prove that the conditions are sufficient.
Received: July 10, 2009
AMS Subject Classification: 05B05, 05B07
Key Words and Phrases: group divisible designs
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 4