Some New Congruences For Overpartition Function With $\ell$-Regular Non-Overlined Parts
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916661975580672 |
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| author | Saikia, Nipen Paksok, Adam |
| author_facet | Saikia, Nipen Paksok, Adam |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_19363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some New Congruences For Overpartition Function With $\ell$-Regular Non-Overlined Parts Saikia, Nipen Paksok, Adam Number Theory 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. |
| title | Some New Congruences For Overpartition Function With $\ell$-Regular Non-Overlined Parts |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.19363 |