Abstract:
We use the quantum statistical approach to estimate the number of restricted plane partitions of an integer $n$ with the number of parts not exceeding some finite $N$. We use the analogy between this number theory problem and the enumeration of microstates of the ideal two-dimensional Bose gas. The numbers of restricted plane partitions calculated with the conjectured expression agree well with the exact values for $n$ from $10$ to $20$.
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