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Asymptotic formulas for integer partitions within the approach of microcanonical ensembleKeywords: integer partitions , plane partition , bosonic systems Abstract: The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary (one-dimensional) partitions, the correction to the leading asymptotic is obtained. The estimate for the number of two-dimensional (plane) partitions coincides with known asymptotic results.
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