On the block structure of proper block designs |
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Authors: | Mike Jacroux |
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Institution: | Washington State University, Pullman, WA 99164-2930, USA |
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Abstract: | In this paper we consider proper block designs and derive an upper bound for the number of blocks which can have a fixed number of symbols common with a given block of the design. To arrive at the desired bound, a generalization of an integer programming theorem due to Bush (1976) is first obtained. The integer programming theorem is then used to derive the main result of this paper. The bound given here is then compared with a similar bound obtained by Kageyama and Tsuji (1977). |
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Keywords: | Primary 62K10 Secondary 62K99 Proper block design Incidence matrix Balanced incomplete block design Partially balanced incomplete block design |
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