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Tricyclic Steiner Triple Systems

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Abstract

A Steiner triple system of order ν, denoted STS(ν), is said to be tricyclic if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this paper we give necessary and sufficient conditions for the existence of a tricyclic STS(ν) for several cases. We also pose conjectures concerning their existence in two remaining cases.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Middle Tennessee State University, Murfreesboro, TN, 37312, USA

    Rebecca C. Calahan

  2. Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN, 37614, USA

    Robert B. Gardner

  3. Department of Statistics, University of Florida, Gainesville, FL, 32611, USA

    Quan D. Tran

Authors
  1. Rebecca C. Calahan
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  2. Robert B. Gardner
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  3. Quan D. Tran
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Correspondence to Robert B. Gardner.

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Calahan, R.C., Gardner, R.B. & Tran, Q.D. Tricyclic Steiner Triple Systems. Graphs and Combinatorics 26, 31–42 (2010). https://doi.org/10.1007/s00373-010-0896-y

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  • DOI: https://doi.org/10.1007/s00373-010-0896-y

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