Asymptotic formulas for the number of the partitions into summands of the form $\lfloorαm\rfloor$

Nian Hong Zhou

Published 2020-08-24Version 1

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 sequence $\{\lfloor\alpha m\rfloor\}_{m\in\mathbb{N}}$. This improves some results of Erd\"{o}s and Richmond established in 1977.