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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 UV. The case where U=V was solved by Lindner and Rosa in 1975. Here, we let UV and completely solve this question for vu=2,4 and for v≥2u−3.

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Correspondence to Eric Mendelsohn.

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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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