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September, 1960 A Generalization of Group Divisible Designs
Damaraju Raghavarao
Ann. Math. Statist. 31(3): 756-771 (September, 1960). DOI: 10.1214/aoms/1177705802


Roy [8] extended the idea of Group Divisible designs of Bose and Connor [1] to $m$-associate classes, calling such designs Hierarchical Group Divisible designs with $m$-associate classes. Subsequently, no literature is found in this direction. The purpose of this paper is to study these designs systematically. A compact definition of the design, under the name Group Divisible $m$-associate (GD $m$-associate) design is given in Section 2. In the same section the parameters of the design are obtained in a slightly different form than that of Roy. The uniqueness of the association scheme from the parameters is shown in Section 3. The designs are divided into $(m + 1)$ classes in Section 4. Some interesting combinatorial properties are obtained in Section 5. The necessary conditions for the existence of a class of these designs are obtained in Section 7. Finally, some numerical illustrations of these designs are given in the Appendix.


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Damaraju Raghavarao. "A Generalization of Group Divisible Designs." Ann. Math. Statist. 31 (3) 756 - 771, September, 1960.


Published: September, 1960
First available in Project Euclid: 27 April 2007

zbMATH: 0232.62034
MathSciNet: MR121925
Digital Object Identifier: 10.1214/aoms/1177705802

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 3 • September, 1960
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