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Near generalized balanced tournament designs with block sizes 4 and 5

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Abstract

A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km + 1, k, k − 1)-BIBD defined on a (km +1)-set V. Its blocks can be arranged into an m × (km + 1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V[x] for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.

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Authors and Affiliations

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

    XiuLing Shan

  2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, China

    XiuLing Shan

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  1. XiuLing Shan
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Correspondence to XiuLing Shan.

Additional information

This work was supported by National Natural Science Foundation of China (Grant Nos. 10771051, 10831002)

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Shan, X. Near generalized balanced tournament designs with block sizes 4 and 5. Sci. China Ser. A-Math. 52, 1927–1938 (2009). https://doi.org/10.1007/s11425-009-0023-9

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  • DOI: https://doi.org/10.1007/s11425-009-0023-9

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