Statistical mechanics approach in the counting of integer partitions

TL;DR

This paper explores integer partitions using statistical mechanics, reproduces known asymptotic results, and proposes a new asymptotic formula for restricted plane partitions based on numerical analysis.

Contribution

It introduces a statistical mechanics framework to analyze integer partitions and conjectures a new asymptotic formula for restricted plane partitions.

Findings

Reproduces known asymptotic results for partitions

Provides numerical evidence for a new asymptotic formula

Suggests a statistical mechanics approach is effective for partition problems

Abstract

The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From numerical analysis of restricted plane partitions an asymptotic formula is conjectured for an intermediate number of parts.