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Balanced ternary designs with block size three

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Combinatorial Mathematics VII

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 829))

Abstract

A balanced ternary design (BTD) is a balanced design on V elements with constant block size in which each element may occur 0, 1 or 2 times in each block. The condition V≡0 (mod 3) is shown to be both necessary and sufficient for the existence of a BTD on V elements with block size 3 and index 2 in which each element is repeated in exactly one block and each element occurs in a constant number of blocks.

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References

  1. W.H. Clatworthy, Tables of two-associate class partially balanced designs, (U.S. Dept. of Commerce, NBS, Washington, 1973).

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  2. I.P. Goulden and R.G. Stanton, Cyclic generation of Steiner triple systems, (to appear).

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  3. Marshall Hall Jr., Combinatorial Theory (Blaisdell, Waltham, Mass., 1967).

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  4. Rev. Thomas Kirkman, On a problem in combinations, Cambridge and Dublin Math. J. 2 (1847), 191–204.

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  5. E. Hastings Moore, Concerning triple systems, Math. Ann. 43 (1893), 271–285.

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  6. Elizabeth J. Morgan, Construction of balanced n-ary designs, Utilitas Math. 11 (1977), 3–31.

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  7. Damaraju Raghavarao, Constructions and combinatorial problems in design of experiments (Wiley, New York, 1971).

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  8. Anne Penfold Street and W.D. Wallis, Combinatorial Theory: An Introduction (Charles Babbage Research Centre, Winnipeg, 1977).

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  9. K.D. Tocher, The design and analysis of block experiments, J. Roy. Statist. Soc. Ser. B 14 (1952), 45–100.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Queensland, St. Lucia, Queensland

    Elizabeth J. Morgan

Authors
  1. Elizabeth J. Morgan
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Editor information

Robert W. Robinson George W. Southern Walter D. Wallis

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© 1980 Springer-Verlag

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Morgan, E.J. (1980). Balanced ternary designs with block size three. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088912

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  • DOI: https://doi.org/10.1007/BFb0088912

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10254-0

  • Online ISBN: 978-3-540-38376-5

  • eBook Packages: Springer Book Archive

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