Enumeration of plane partitions with a restricted number of parts

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 $n=10÷20$.

10 pages

References in corpus (5)

• Boxed Plane Partitions as an Exactly Solvable Boson Model
• Asymptotics of the number partitioning distribution
• Fractional statistics and finite bosonic system: A one-dimensional case
• Gentile statistics and restricted partitions
• Asymptotic formulas for integer partitions within the approach of microcanonical ensemble

Cited by in corpus (1)

• A statistical mechanical approach to restricted integer partition functions