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Mathematics  2014 

Enumeration of plane partitions with a restricted number of parts

DOI: 10.1007/s11232-014-0223-5

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Abstract:

In the paper, the quantum-statistical approach is used to estimate the number of restricted plane partitions of an integer $n$ with the number of parts not exceeding some finite $N$. The analogy between this number-theoretical problem and the enumeration of microstates of the ideal two-dimensional Bose-gas is used. The conjectured expression for the number of restricted plane partitions shows a good agreement between calculated and exact values for $n=10\div20$.

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