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arXiv · 2109.10344

Distribution of certain $\ell$-regular partitions and triangular numbers

Chiranjit Ray
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Abstract

Let $pod_{\ell}(n)$ be the number of $\ell$-regular partitions of $n$ with distinct odd parts. In this article, prove that for any positive integer $k$, the set of non-negative integers $n$ for which $pod_{\ell}(n)\equiv 0 \pmod{p^{k}}$ has density one under certain conditions on $\ell$ and $p$. For $p \in \{3,5,7\}$, we also exhibit multiplicative identities for $pod_{p}(n)$ modulo $p.$

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Chiranjit Ray. 2021-09-21. Distribution of certain $\ell$-regular partitions and triangular numbers. https://arxiv.org/abs/2109.10344

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