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arXiv · 2504.01518

On 2-color partitions where one of the colors is multiples of $7^k$

D. S. Gireesh·Shivashankar C.·HemanthKumar B
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Abstract

In this work, we investigate the arithmetic properties of $p_{1,7^k}(n)$, which counts 2-color partitions of $n$ where one of the colors appears only in parts that are multiples of $7^k$. By constructing generating functions for $p_{1,7^k}(n)$ across specific arithmetic progressions, we establish a set of Ramanujan-type infinite family of congruences modulo powers of $7$.

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D. S. Gireesh, Shivashankar C., HemanthKumar B. 2025-04-02. On 2-color partitions where one of the colors is multiples of $7^k$. https://arxiv.org/abs/2504.01518

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