Summary
A necessary and sufficient condition for the connectedness ofm-associate partially balanced incomplete block (PBIB) designs having an asymmetrical association scheme is given, only in terms of design parameters, without inner structure parameters of designs.
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References
Aggarwal, K. R. and Raghavarao, D. (1972). Residue classes PBIB designs,Calcutta Statist. Assoc. Bull.,21, 63–69.
Bose, R. C. (1950).Least Squares Aspects of Analysis of Variance, Institute of Statistics, Univ. of North Carolina.
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. (1982). Connectedness of two-associate PBIB designs,J. Statist. Plann. Inf.,7, 77–82.
Mohan, N. R. (1981). A criterion for connectedness in two-associate class PBIB designs,J. Statist. Plann. Inf.,5, 211–212.
Nair, C. R. (1964). A new class of designs,J. Amer. Statist. Assoc.,59, 817–833.
Ogawa, J., Ikeda, S. and Kageyama, S. (1984). Connectedness of PBIB designs with applications, (to appear in theProceedings of the Shrikhande Seminar at Indian Statistical Institute), Calcutta, India, December, 1982.
Patwardhan, G. A. and Vartak, M. N. (1981). On the adjugate of a symmetrical balanced incomplete block design with λ=1, Combinatorics and Graph Theory, 133–152,Lecture Notes in Mathematics,885, Springer-Verlag, New York.
Raghavarao, D. (1971).Constructions and Combinatorial Problems in Design of Experiments, Wiley, New York.
Saha, G. M. and Kageyama, S. (1984). Connectedness-conditions of PBIB designs,J. Japan. Statist. Soc.,14, 169–178.
Shah, B. V. (1959). A generalization of partially balanced incomplete block designs,Ann. Math. Statist.,30, 1041–1050.
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Supported in part by Grant 321-6066-58530013 (Japan).
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Kageyama, S. Connectedness of PBIB designs having asymmetrical association schemes. Ann Inst Stat Math 37, 139–143 (1985). https://doi.org/10.1007/BF02481086
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DOI: https://doi.org/10.1007/BF02481086