Table of Contents
ISRN Discrete Mathematics
Volume 2012, Article ID 251457, 7 pages
http://dx.doi.org/10.5402/2012/251457
Research Article

Pairwise Balanced Design of Order and 2-Fold System of Order

1Department of Mathematics, University of Kalyani, Kalyani 741235, India
2Department of Mathematics, National Institute of Technology, Burdwan, Durgapur 713209, India

Received 4 September 2012; Accepted 23 October 2012

Academic Editors: Y. Hou and M. Pal

Copyright © 2012 Manjusri Basu et al. 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

In the Steiner triple system, Bose (1939) constructed the design for and later on Skolem (1958) constructed the same for . In the literature we found a pairwise balanced design (PBD) for . We also found the 2-fold triple system of the orders 3n and . In this paper, we construct a PBD for and a 2-fold system of the order . The second construction completes the 2-fold system for all .