On the embeddings of mendelsohn triple systems |
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Authors: | Shen Hao |
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Institution: | (1) Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai, China |
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Abstract: | It is proved in this paper that there exists an incomplete Mendelsohn triple system IMTS(u,v; λ) if and only ifλ(u-v)(u-2v-1)≡0(mod 3),u≥2v+1 and (u, v, λ) ≠ (6, 1, 1). As a consequence, it is proved that for any given λ≥1, a Mendelsohn triple system MTS (v, λ) can be embedded in an MTS (u, λ) if and only ifλu(u-1)≡0(mod 3) andu≥2v+1.
Project supported by the National Natural Science Foundation of China. |
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