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A singular direct product for quadruple systems

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

Abstract

A Steiner quadruple system is an ordered pair (X,Q) where X is a finite set and Q is a set of 4-subsets of X such that every 3-subset of X is contained in a unique member of Q.

This paper gives a structure for studying all the known recursive constructions for quadruple systems. The structure is then applied to existence problems for quadruple systems with subsystems.

Keywords

  • Induction Hypothesis
  • Unique Member
  • Existence Problem
  • Direct Construction
  • Recursive Construction

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.

This work forms part of the author's research towards a Ph.D. at the University of Newcastle.

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References

  1. S. O. Aliev, Symmetric algebras and Steiner systems, Soviet Math. Dokl. 8 (1967), 651–653.

    MATH  Google Scholar 

  2. H. Hanani, On quadruple systems, Can. J. Math. 12 (1960), 145–157.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. A. Hartman, Tripling quadruple systems, Ars Combinatoria (to appear).

    Google Scholar 

  4. A. Hartman, Construction and resolution of quadruple systems, Ph.D. Thesis, University of Newcastle, Australia, 1980.

    MATH  Google Scholar 

  5. C. C. Lindner and A. Rosa, Steiner quadruple systems—a survey, Discrete Math. 22 (1978), 147–181.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. K. T. Phelps, Rotational quadruple systems, Ars Combinatoria 4 (1977), 177–185.

    MathSciNet  MATH  Google Scholar 

  7. B. Rokowska, Some new constructions of 4-tuple systems, Colloq. Math. 17 (1967), 111–121.

    MathSciNet  MATH  Google Scholar 

  8. J. Steiner, Combinatorische Ausgabe, J. Reine Angew. Math. 45 (1853), 181–182.

    CrossRef  MathSciNet  Google Scholar 

  9. W.S.B. Woolhouse, Prize question 1733, Lady's and Gentlemen's diary (1844).

    Google Scholar 

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© 1981 Springer-Verlag

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Hartman, A. (1981). A singular direct product for quadruple systems. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091821

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  • DOI: https://doi.org/10.1007/BFb0091821

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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