A Generalization of Group Divisible Designs
Raghavarao, Damaraju
Ann. Math. Statist., Tome 31 (1960) no. 4, p. 756-771 / Harvested from Project Euclid
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.
Publié le : 1960-09-14
Classification: 
@article{1177705802,
     author = {Raghavarao, Damaraju},
     title = {A Generalization of Group Divisible Designs},
     journal = {Ann. Math. Statist.},
     volume = {31},
     number = {4},
     year = {1960},
     pages = { 756-771},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177705802}
}
Raghavarao, Damaraju. A Generalization of Group Divisible Designs. Ann. Math. Statist., Tome 31 (1960) no. 4, pp.  756-771. http://gdmltest.u-ga.fr/item/1177705802/