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Tripling Construction for Large Sets of Resolvable Directed Triple Systems

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Abstract

In this paper, we first define a doubly transitive resolvable idempotent quasigroup (DTRIQ), and show that a DTRIQ of order v exists if and only if v ≡ 0 (mod 3) and v ≢ 2 (mod 4). Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang (J. Combin. Designs, 4 (1996), 301–321). As an application, we obtain an LRDTS(4 · 3n) for any integer n ≥ 1, which provides an infinite family of even orders.

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Authors and Affiliations

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

    Jun Ling Zhou & Yan Xun Chang

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  1. Jun Ling Zhou
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  2. Yan Xun Chang
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Correspondence to Jun Ling Zhou or Yan Xun Chang.

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Supported by TRAPOYT and NSFC Grant No. 10371002

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Zhou, J.L., Chang, Y.X. Tripling Construction for Large Sets of Resolvable Directed Triple Systems. Acta Math Sinica 22, 311–318 (2006). https://doi.org/10.1007/s10114-004-0470-8

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  • DOI: https://doi.org/10.1007/s10114-004-0470-8

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