Skip to main content
Log in

Connectedness of PBIB designs having asymmetrical association schemes

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aggarwal, K. R. and Raghavarao, D. (1972). Residue classes PBIB designs,Calcutta Statist. Assoc. Bull.,21, 63–69.

    Article  MathSciNet  Google Scholar 

  2. Bose, R. C. (1950).Least Squares Aspects of Analysis of Variance, Institute of Statistics, Univ. of North Carolina.

  3. 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.

    Article  MathSciNet  Google Scholar 

  4. Kageyama, S. (1982). Connectedness of two-associate PBIB designs,J. Statist. Plann. Inf.,7, 77–82.

    Article  MathSciNet  Google Scholar 

  5. Mohan, N. R. (1981). A criterion for connectedness in two-associate class PBIB designs,J. Statist. Plann. Inf.,5, 211–212.

    Article  MathSciNet  Google Scholar 

  6. Nair, C. R. (1964). A new class of designs,J. Amer. Statist. Assoc.,59, 817–833.

    Article  MathSciNet  Google Scholar 

  7. 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.

  8. 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.

    MATH  Google Scholar 

  9. Raghavarao, D. (1971).Constructions and Combinatorial Problems in Design of Experiments, Wiley, New York.

    MATH  Google Scholar 

  10. Saha, G. M. and Kageyama, S. (1984). Connectedness-conditions of PBIB designs,J. Japan. Statist. Soc.,14, 169–178.

    MathSciNet  MATH  Google Scholar 

  11. Shah, B. V. (1959). A generalization of partially balanced incomplete block designs,Ann. Math. Statist.,30, 1041–1050.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by Grant 321-6066-58530013 (Japan).

About this article

Cite this article

Kageyama, S. Connectedness of PBIB designs having asymmetrical association schemes. Ann Inst Stat Math 37, 139–143 (1985). https://doi.org/10.1007/BF02481086

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02481086

Key words and phrases

Navigation