Enumeration of plane partitions with a restricted number of parts

الأصل · EN

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=1020.