Note on partitions into polynomials with number of parts in an arithmetic progression

16 Feb 2020 Zhou Nian Hong

Let $f: \mathbb{Z}_+\rightarrow \mathbb{Z}_+$ be a polynomial with the property that corresponding to every prime $p$ there exists an integer $\ell$ such that $p\nmid f(\ell)$. In this paper, we establish some equidistributed results between the number of partitions of integer $n$ whose parts taken from the sequence $\{f(\ell)\}_{\ell=1}^{\infty}$ and the number of parts of those partitions are in certain arithmetic progression...

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