Partitions with parts in a finite set

TL;DR

This paper derives an asymptotic formula for counting partitions of integers with parts in a finite set of relatively prime positive integers using elementary arithmetic methods.

Contribution

It provides a new elementary arithmetic approach to obtain asymptotic formulas for partition functions constrained to finite sets.

Findings

Derived an asymptotic formula for p_A(n)

Applied elementary arithmetic techniques

Enhanced understanding of partition functions with restricted parts

Abstract

Let A be a nonempty finite set of relatively prime positive integers, and let p_A(n) denote the number of partitions of n with parts in A. An elementary arithmetic argument is used to obtain an asymptotic formula for p_A(n).