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On tactical configurations with no four-cycles

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Elsevier
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Abstract

An improved lower bound is given for the band sizes of tactical configurations of rank exceeding two having no 4-cycles. This bound is applied to find an optimal configuration with certain specified parameters. A formula is given for the maximum number of cycle types one must examine to demonstrate that a rank r configuration has no g-cycle. This result, which has appeared in our earlier work as the number of types of closed walks, answers a question of Longyear.

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