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Aequationes mathematicae

, Volume 85, Issue 3, pp 347–358 | Cite as

Configurations in bowtie systems

  • M. J. Grannell
  • T. S. Griggs
  • G. Lo Faro
  • A. Tripodi
Article
  • 97 Downloads

Abstract

There are ten configurations of two bowties that can arise in a bowtie system. We determine a basis for configurations of two bowties in both balanced and general bowtie systems. We also determine the avoidance spectrum for the three most compact configurations of two bowties.

Mathematics Subject Classification (2010)

Primary 05B30 Secondary 05B05 05B07 

Keywords

Bowtie system configuration Steiner triple system 

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References

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    Colbourn, C.J., Dinitz, J.H. (eds.): The Handbook of Combinatorial Designs. 2nd edn. CRC Press, Boca Raton (2007)Google Scholar
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    Colbourn C.J., Rosa A.: Triple Systems. Clarendon Press, New York (1999)MATHGoogle Scholar
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    Grannell M.J., Griggs T.S., Lo Faro G., Tripodi A.: Small bowtie systems: an enumeration. J. Combin. Math. Combin. Comput. 70, 149–159 (2009)MathSciNetMATHGoogle Scholar
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    Grannell M.J., Griggs T.S., Mendelsohn E.: A small basis for four-line configurations in Steiner triple systems. J. Combin. Des. 3, 51–59 (1994)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  • M. J. Grannell
    • 1
  • T. S. Griggs
    • 1
  • G. Lo Faro
    • 2
  • A. Tripodi
    • 2
  1. 1.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUK
  2. 2.Dipartimento di Matematica e InformaticaUniversitá di Messina Contrada PapardoMessinaItaly

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