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Large sets of pure directed triple systems with index λ

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Abstract

A directed triple system of order v with index λ, briefly by DTS(v, λ), is a pair (X, B) where X is a v-set and B is a collection of transitive triples (blocks) on X such that every ordered pair of X belongs to λ blocks of B. A simple DTS(v, λ) is a DTS(v, λ) without repeated blocks. A simple DTS(v, λ) is called pure and denoted by PDTS(v, λ) if (x, y, z)∈B implies (z, y, x), (z, x, y), (y, x, z), (y, z, x), (x, z, y) ∉ B. A large set of disjoint PDTS(v, λ), denoted by LPDTS(v, λ), is a collection of 3(v−2)/λ disjoint pure directed triple systems on X. In this paper, some results about the existence for LPDTS(v, λ) are presented. Especially, we determine the spectrum of LPDTS(v, 2).

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Authors and Affiliations

  1. Institute of Mathematics, Beijing Jiaotong University, Beijing, 100044, P. R. China

    Bing Li Fan & Jun Ling Zhou

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  1. Bing Li Fan
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  2. Jun Ling Zhou
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Correspondence to Bing Li Fan.

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Supported by National Natural Science Foundation of China (Grant Nos. 10771013 and 10831002)

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Fan, B.L., Zhou, J.L. Large sets of pure directed triple systems with index λ. Acta. Math. Sin.-English Ser. 26, 1899–1914 (2010). https://doi.org/10.1007/s10114-010-9249-2

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  • DOI: https://doi.org/10.1007/s10114-010-9249-2

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