Near generalized balanced tournament designs with block sizes 4 and 5 |
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Authors: | XiuLing Shan |
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Affiliation: | 1.Department of Mathematics,Beijing Jiaotong University,Beijing,China;2.College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang,China |
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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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