Partitions into Beatty sequences

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 Erdös and Richmond established in 1977.

13 pages, changed the title