Article

Theoretical and Mathematical Physics

, Volume 181, Issue 2, pp 1428-1434

First online:

Enumeration of plane partitions with a restricted number of parts

  • A. A. RovenchakAffiliated withDepartment for Theoretical Physics, Ivan Franko National University of Lviv Email author 

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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.

Keywords

Bose gas plane partition restricted partition