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arXiv · 2503.02366

On $7^k$-regular partitions modulo powers of $7$

D. S. Gireesh·HemanthKumar B
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Abstract

In this study, we explore the arithmetic properties of $b_{7^k}(n)$ for any $k\geq1$, which enumerates the partitions of $n$ where no part is divisible by $7^k$. By constructing generating functions for $b_{7^k}(n)$ over specific arithmetic progressions, we establish a collection of Ramanujan-type congruences.

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BibTeXRIS

D. S. Gireesh, HemanthKumar B. 2025-03-04. On $7^k$-regular partitions modulo powers of $7$. https://arxiv.org/abs/2503.02366

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