Divisibility properties of weighted $k$ regular partitions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908692589314048 |
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| author | Banerjee, Debika Kane, Ben |
| author_facet | Banerjee, Debika Kane, Ben |
| contents | We study a generalized class of weighted $k$-regular partitions defined by \[ \sum_{n=0}^{\infty} c_{k, r_1, r_2}(n) q^n = \prod_{n=1}^{\infty} \frac{(1 - q^{nk})^{r_1}}{(1 - q^n)^{r_2}}, \] which extends the classical $k$-regular partition function $b_k(n)$. We establish new infinite families of Ramanujan-type congruences, divisibility results, and positive-density prime sets for which $c_{k, r_1, r_2}(n)$ vanishes modulo a given prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Divisibility properties of weighted $k$ regular partitions Banerjee, Debika Kane, Ben Number Theory Combinatorics 05A17, 11P81, 11P83, 11F11 We study a generalized class of weighted $k$-regular partitions defined by \[ \sum_{n=0}^{\infty} c_{k, r_1, r_2}(n) q^n = \prod_{n=1}^{\infty} \frac{(1 - q^{nk})^{r_1}}{(1 - q^n)^{r_2}}, \] which extends the classical $k$-regular partition function $b_k(n)$. We establish new infinite families of Ramanujan-type congruences, divisibility results, and positive-density prime sets for which $c_{k, r_1, r_2}(n)$ vanishes modulo a given prime. |
| title | Divisibility properties of weighted $k$ regular partitions |
| topic | Number Theory Combinatorics 05A17, 11P81, 11P83, 11F11 |
| url | https://arxiv.org/abs/2508.20573 |