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On Transversal Designs

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Combinatorics

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 16))

Abstract

A design is a pair (X,B) where X is a finite set of points and B is a family of not necessarily distinct- subsets Bi (called blocks) of X.

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References

  1. Bose, R.C., E.T. Parker & S.S. Shrikhande, Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture, Canad. J. Math., 12 (1960) 189–203.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bose, R.C. & S.S. Shrikhande, On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler. Trans. Amer. Math. Soc., 95 (1960) 191–209.

    Article  MathSciNet  MATH  Google Scholar 

  3. Chowla, S., P. Erdös & E.G. Strauss, On the maximal number of pairwise orthogonal Latin squares of a given order, Canad. J. Math., 12 (1960) 204–208.

    Article  MathSciNet  MATH  Google Scholar 

  4. Dulmage, A.L., D.M. Johnson & N.S. Mendelsohn, Orthomorphisms of groups and orthogonal Latin squares, I, Canad. J. Math., 13 (1961) 356–372.

    Article  MathSciNet  MATH  Google Scholar 

  5. Hanani, H., On the number of orthogonal Latin squares, J. Combinatorial Theory, 8 (1970) 247–271.

    Article  MathSciNet  MATH  Google Scholar 

  6. MacNeish, H.F., Euler squares, Ann. of Math., 23 (1922) 221–227.

    Article  MathSciNet  Google Scholar 

  7. Parker, E., Construction of some sets of mutually orthogonal Latin squares, Proc. Amer. Math. Soc., 10 (1959) 946–949.

    Article  MathSciNet  MATH  Google Scholar 

  8. Raghavarao, D., Constructions and combinatorial problems in design of experiments, J. Wiley & Sons, New York, 1971.

    MATH  Google Scholar 

  9. Rogers, K., A note on orthogonal Latin squares, Pacific J. Math., 14 (1964) 1395–1397.

    MathSciNet  MATH  Google Scholar 

  10. Wilson, R.M., Concerning the number of mutually orthogonal Latin squares, in print.

    Google Scholar 

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M. Hall Jr. J. H. van Lint

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© 1975 Mathematical Centre, Amsterdam

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Hanani, H. (1975). On Transversal Designs. In: Hall, M., van Lint, J.H. (eds) Combinatorics. NATO Advanced Study Institutes Series, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1826-5_3

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  • DOI: https://doi.org/10.1007/978-94-010-1826-5_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1828-9

  • Online ISBN: 978-94-010-1826-5

  • eBook Packages: Springer Book Archive

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