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A singular direct product for quadruple systems

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Combinatorial Mathematics VIII

Part of the book series: Lecture Notes in Mathematics ((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.

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.

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Author information

Authors and Affiliations

  1. Department of Combinatories and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    A. Hartman

Authors
  1. A. Hartman
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Editor information

Kevin L. McAvaney

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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

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