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Distributive block structures and their automorphisms

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 884)

Abstract

The experimental units in a statistical experiment are frequently grouped into blocks in one or more ways. When the different families of blocks fit together in a well-behaved way we have a distributive block structure. We show that the orbits of the automorphism group of a distributive block structure on pairs of experimental units are precisely the sets which the combinatorial structure leads one to expect. Possible generalizations of this result are discussed.

Keywords

  • Equivalence Relation
  • Automorphism Group
  • Experimental Unit
  • Block Structure
  • Isomorphism Class

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. R.A. Bailey, Latin squares with highly transitive automorphism groups, to appear.

    Google Scholar 

  2. R.A. Bailey, A unified approach to design of experiments, J.R. Statist. Soc. A, to appear.

    Google Scholar 

  3. W.C. Holland, The characterization of generalized wreath products, J. Algebra 13 (1969), 152–172.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. P.W.M. John, Statistical design and analysis of experiments. (Macmillan, 1971.)

    Google Scholar 

  5. O. Kempthorne, The design and analysis of experiments. (Wiley, 1957.)

    Google Scholar 

  6. J.A. Nelder, The analysis of randomized experiments with orthogonal block structure, Proc. Roy. Soc. A 283 (1965), 147–178.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. T. P. Speed and R.A. Bailey, On a class of association schemes derived from lattices of equivalence relations, Proceedings of the First Western Australian Algebra Conference (1980).

    Google Scholar 

  8. T.N. Trockmorton, Structures of classification data. Ph.D. Thesis, Iowa State University, 1961.

    Google Scholar 

  9. F. Yates, The formation of Latin squares for use in field experiments, Empire J. Exp. Agric. 1, (1933), 235–244.

    Google Scholar 

  10. G. Zyskind, Error structures in experimental designs. Ph.D. Thesis, Iowa State University, 1958.

    Google Scholar 

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© 1981 Springer-Verlag

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Bailey, R.A. (1981). Distributive block structures and their automorphisms. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091813

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  • DOI: https://doi.org/10.1007/BFb0091813

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10883-2

  • Online ISBN: 978-3-540-38792-3

  • eBook Packages: Springer Book Archive