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arXiv · 2508.20573

Divisibility properties of weighted $k$ regular partitions

Debika Banerjee·Ben Kane
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Abstract

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.

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Debika Banerjee, Ben Kane. 2025-08-28. Divisibility properties of weighted $k$ regular partitions. https://arxiv.org/abs/2508.20573

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