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In this paper we find generating functions and asymptotic expressions for the number of partitions of a positive integer n into two sets of positive integers satisfying the conditions The set ‘ b ’ can be empty. Such partitions are considered by Temperley (1) in a forth-coming paper on the roughness of crystal surfaces. We shall consider them in more detail and under different sets of conditions on the a 's and b 's.
F. C. Auluck (Mon,) studied this question.