International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 148580, 10 pages
http://dx.doi.org/10.1155/2011/148580
Research Article

Group Divisible Designs with Two Associate Classes and 𝜆 2 = 1

Nittiya Pabhapote1 and Narong Punnim2

1Department of Mathematics, University of the Thai Chamber of Commerce, Dindaeng, Bangkok 10400, Thailand
2Department of Mathematics, Srinakharinwirot University, Sukhumvit 23, Bangkok 10110, Thailand

Received 28 January 2011; Accepted 19 May 2011

Academic Editor: Michael Tom

Copyright © 2011 Nittiya Pabhapote and Narong Punnim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The original classiffcation of PBIBDs defined group divisible designs GDD( 𝑣 = 𝑣 1 + 𝑣 2 + ⋯ + 𝑣 𝑔 , 𝑔 , 𝑘 , 𝜆 1 , 𝜆 2 ) with 𝜆 1 ≠ 0 . In this paper, we prove that the necessary conditions are suffcient for the existence of the group divisible designs with two groups of unequal sizes and block size three with 𝜆 2 = 1 .