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Association schemes of new types and necessary conditions for existence for regular and symmetrical PBIB designs with those association schemes

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References

  1. R. C. Bose and M. Mesner, “On linear associative algebras corresponding to association schemes of partially balanced designs,”Ann. Math. Statist., 30 (1959), 21–38.

    Article  MATH  MathSciNet  Google Scholar 

  2. W. S. Connor and W. R. Clatworthy, “Some theorems for partially balanced designs,”Ann. Math. Statist., 25 (1954), 100–112.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. W. Jones,The Arithmetic Theory of Quadratic Forms, John Wiley & Sons, Inc., 1950.

  4. D. Raghavarao, “A generalization of group divisible designs,”Ann. Math. Statist., 31 (1960), 756–771.

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Raghavarao and K. Chandrasekhararao, “Cubic designs,”Ann. Math. Statist., 35 (1964), 389–397.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. V. Shah, “On a generalization of the Kronecker product designs,”Ann. Math. Statist., 30 (1959), 48–54.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. K. Tharthare, “Right angular desings,”Ann. Math. Statist., 34 (1963), 1057–1067.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. n. Vartak, “On an application of Kronecker product of matrices to statistical designs,”Ann. Math. Statist., 26 (1955), 420–436.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. N. Vartak, “The non-existence of certain PBIB designs,”Ann. Math. Statist., 30 (1959), 1051–1062.

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Yamamoto and Y. Fujii, “Analysis of partially balanced incomplete block designs,”J. Sci. Hiroshima Univ., Ser. A-I 27 (1963), 119–135.

    MATH  MathSciNet  Google Scholar 

  11. S. S. Schrikhande, D. Raghavarao and S. K. Tharthare, “Non-existence of some unsymmetrical partially balanced incomplete block designs,”Canad. J. Math., 15 (1963), 686–701.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Wakayama Medical College, Wakayama, Japan

    Kumaichi Kusumoto

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  1. Kumaichi Kusumoto
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Kusumoto, K. Association schemes of new types and necessary conditions for existence for regular and symmetrical PBIB designs with those association schemes. Ann Inst Stat Math 19, 73–100 (1967). https://doi.org/10.1007/BF02911669

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  • DOI: https://doi.org/10.1007/BF02911669

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