Combinatorial methods in the theory of dams

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Abstract
In this paper we shall be concerned with two mathematical models of infinite dams. In the first model independent random inputs occur at regular time intervals and in the second model independent random inputs occur in accordance with a Poisson process. The first model has already been studied by Gani, Yeo and others, and the second model by Gani and Prabhu, Gani and Pyke, Kendall, and others. For both models we shall find explicit formulas for the distribution of the content of the dam and that of the lengths of the wet periods and dry periods. The proofs are elementary and based on two generalizations of the classical ballot theorem.

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