Partitions into Beatty sequences

TL;DR

This paper derives asymptotic formulas for counting partitions of integers into Beatty sequence elements, improving upon classical results by Erdős and Richmond from 1977.

Contribution

It provides new asymptotic formulas for partitions into Beatty sequences, extending and refining previous classical results.

Findings

Asymptotic formulas for partitions into Beatty sequences derived

Results apply to both summands and distinct summands

Improves classical results from 1977 by Erdős and Richmond

Abstract

Let $\alpha>1$ be an irrational number. We establish asymptotic formulas for the number of partitions of $n$ into summands and distinct summands, chosen from the Beatty sequence $(\lfloor\alpha m\rfloor)_{m\in\mathbb{N}}$. This improves some results of Erd\"{o}s and Richmond established in 1977.