Partitions into Beatty sequences

Nian Hong Zhou

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arXiv · 2008.10500

Partitions into Beatty sequences

Nian Hong Zhou

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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.

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Nian Hong Zhou. 2020-08-24. Partitions into Beatty sequences. https://arxiv.org/abs/2008.10500

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