Abstract
In this paper it is shown that a regular group divisible (GD) design, with parametersv, b, r, k, λ 1, λ2 satisfyingrk − λ2 v + 1 andλ 2 = λ1 + 1, must be symmetric (i.e.,v + b). Furthermore, the parameters of such symmetric regular GD designs can be expressed in terms of only two integral parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Clatworthy, W.H.: Tables of Two-Associate-Class Partially Balanced Designs. Applied Mathematics Series 63. Washington, D.C.: NBS 1973
John, J.A., Turner, G.: Some new group divisible designs. J. Stat. Plann. Inference1, 103–107 (1977)
Raghavarao, D.: Constructions and Combinatorial Problems in Design of Experiments. New York: John Wiley & Sons 1971
Shrikhande, S.S.: Affine resolvable balanced incomplete block designs; a survey. Aequationes Math.14, 251–269 (1976)
Author information
Authors and Affiliations
Additional information
Supported in part by Grant 59540043 (C), Japan.
Rights and permissions
About this article
Cite this article
Bhagwandas, Kageyama, S. & Mukerjee, R. Symmetry and classification of certain regular group divisible designs. Graphs and Combinatorics 2, 15–20 (1986). https://doi.org/10.1007/BF01788072
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01788072