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On the Intersection Problem for Steiner Triple Systems of Different Orders

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Abstract

A Steiner triple system of order v, or STS(v), is a pair (V, ) with V a set of v points and a set of 3-subsets of V called blocks or triples, such that every pair of distinct elements of V occurs in exactly one triple. The intersection problem for STS is to determine the possible numbers of blocks common to two Steiner triple systems STS(u), (U, ), and STS(v), (V, ), with U⊆V. The case where U=V was solved by Lindner and Rosa in 1975. Here, we let U⊂V and completely solve this question for v−u=2,4 and for v≥2u−3.

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Authors and Affiliations

  1. Department of Mathematics, Ryerson University, Toronto, ON, M5B 2K3, Canada

    Peter Danziger

  2. Department of Mathematics, University of Victoria, Victoria, BC, V8W 3P4, Canada

    Peter Dukes

  3. Department of Pure Mathematics Walton Hall, The Open University, Milton Keynes, MK7 6AA, UK

    Terry Griggs

  4. Department of Mathematics, University of Toronto, Toronto, ON, M5S 3G3, Canada

    Eric Mendelsohn

Authors
  1. Peter Danziger
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  2. Peter Dukes
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  3. Terry Griggs
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  4. Eric Mendelsohn
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Corresponding author

Correspondence to Eric Mendelsohn.

Additional information

supported by NSERC research grant #OGP0170220.

supported by NSERC postdoctoral fellowship.

supported by NSERC research grant #OGP007621.

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Danziger, P., Dukes, P., Griggs, T. et al. On the Intersection Problem for Steiner Triple Systems of Different Orders. Graphs and Combinatorics 22, 311–329 (2006). https://doi.org/10.1007/s00373-006-0664-1

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  • DOI: https://doi.org/10.1007/s00373-006-0664-1

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