IJPAM: Volume 55, No. 4 (2009)

GROUP DIVISIBLE DESIGNS WITH
TWO ASSOCIATE CLASSES AND $\lambda_2=2$

Chariya Uiyyasathian$^1$, Wannee Lapchinda$^2$
$^1$Department of Mathematics
Faculty of Science
Chulalongkorn University
Paya Mai Road, Patumwan, Bangkok, 10330, THAILAND
$^{1}$National Center of Excellence in Mathematics
PERDO
Bangkok, 10400, THAILAND
e-mail: chariya.u@chula.ac.th
$^2$School of Science
University of the Thai Chamber of Commerce
Dindaeng, Bangkok, 10400, THAILAND
e-mail: wannee_lap@utcc.ac.th


Abstract.A group divisible design GDD $(v, g, k, \lambda_1, \lambda_2)$ is a collection of $k$-subsets (called blocks) of a $v$-set of symbols where the $v$-set is divided into $g$ groups: each pair of symbols from the same group occurs in exactly $\lambda_1$ blocks, and each pair of symbols from different groups occurs in exactly $\lambda_2$ blocks. Here, we focus on an existence problem of GDDs with two associate classes or when $g=2$, and with blocks of size 3, when the required designs have two groups of unequal sizes and $\lambda_2=2$. We obtain the necessary conditions and prove that these conditions are sufficient.

Received: August 17, 2009

AMS Subject Classification: 05B05, 51E10

Key Words and Phrases: group divisible designs

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 4