A statistical mechanical approach to restricted integer partition functions

Abstract

The main aim of this paper is twofold: (1) Suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions --- a way of writing an integer as a sum of other integers under certain restrictions. In this approach, the generating function of restricted integer partition functions is constructed from the canonical partition functions of various quantum gases. (2) Introducing a new type of restricted integer partition functions corresponding to general statistics which is a generalization of Gentile statistics in statistical mechanics; many kinds of restricted integer partition functions are special cases of this restricted integer partition function. Moreover, with statistical mechanics as a bridge, we reveals a mathematical fact: the generating function of restricted integer partition function is just the symmetric function which is a class of functions being invariant under the action of permutation groups. Using the approach, we provide some expressions of restricted integer partition functions as examples.

References in corpus (3)

• Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum (su(2)) algebra
• From creation and annihilation operators to statistics
• Asymptotic formulas for integer partitions within the approach of microcanonical ensemble

Cited by in corpus (4)

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• Unified framework for generalized quantum statistics: canonical partition function, maximum occupation number, and permutation phase of wave function
• Scattering approach for calculating one-loop effective action and vacuum energy
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