Some New Congruences For Overpartition Function With $\ell$-Regular Non-Overlined Parts

Nipen Saikia; Adam Paksok

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arXiv · 2503.19363

Some New Congruences For Overpartition Function With $\ell$-Regular Non-Overlined Parts

Nipen Saikia·Adam Paksok

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Abstract

Alanzi et al. (2022) investigated overpartition of a positive integer $n$ with $\ell$-regular non-overlined parts denoted by $\overline R_\ell^\ast (n)$, and proved some results for the case $\ell=3$. As extension to the results of Alanzi et al., Sellers (2024) proved some new congruences for $\overline R_3^\ast (n)$. In this paper, we prove some new infinite families and particular congruences for $\overline R_\ell^\ast (n)$ for $\ell=4, 5k, 6$, and 8, where $k$ is any positive integer. We also offer some congruences connecting $\overline R_\ell^\ast (n)$ with some other partition functions.

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BibTeX RIS

Nipen Saikia, Adam Paksok. 2025-03-25. Some New Congruences For Overpartition Function With $\ell$-Regular Non-Overlined Parts. https://arxiv.org/abs/2503.19363

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