Abstract
The necessary and sufficient conditions for m-associate partially balanced block (PBB) designs to be connected are given. This generalizes the criterion for m-associate partially balanced incomplete block (PBIB) designs, which has originally been established by Ogawa, Ikeda and Kageyama (1984, Proceedings of the Seminar on “Combinatorics and Applications”, 248–255, Statistical Publishing Society, Calcutta).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baksalary, J. K. and Tabis, Z. (1987). A note on connectedness of PBIB designs, Canad. J. Math., 15, 147–150.
Bose, R. C. and Mesner, D. M. (1959). On linear associative algebras corresponding to association schemes of partially balanced designs, Ann. Math. Statist., 30, 21–38.
Kageyama, S. (1974). Reduction of associate classes for block designs and related combinatorial arrangements, Hiroshima Math. J., 4, 527–618.
Ogawa, J., Ikeda, S. and Kageyama, S. (1984). Connectedness of PBIB designs with applications, Proc. Seminar on “Combinatorics and Applications” in Honour of Professor S. S. Shrikhande on His 65th Birthday, December 14–17, 1982, Indian Statistical Institute, 248–255, Statistical Publishing Society, Calcutta, India.
Saha, G. M. and Kayeyama, S. (1984). Connectedness-conditions of PBIB designs, J. Japan Statist. Soc., 14, 169–178.
Vartak, M. N. (1955). On an application of Kronecker product of matrices to statistical designs. Ann. Math. Statist., 26, 420–438.
Author information
Authors and Affiliations
Additional information
This work was partially supported by the Polish Academy of Sciences Grant No. MR I.1-2/2.
About this article
Cite this article
Brzeskwiniewicz, H. On the connectedness of partially balanced block designs. Ann Inst Stat Math 41, 199–204 (1989). https://doi.org/10.1007/BF00049118
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00049118