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arXiv · 2505.12270

Arithmetic properties of $(\ell,m)$-regular colored partitions

Yashas N.·C. Shivashankar·S. Chandankumar
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Abstract

Let $b^{k}_{\ell,m}(n)$ denotes the number of $k-$colored partitions of $n$ into parts that are not multiples of $\ell$ or $m$. We establish several congruence relations for $b_{\ell,m}(n)$. For instance, for any nonnegative integer $n$ $$b^{2}_{4,5}(8n+7) \equiv 0 \pmod{40}.$$

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Yashas N., C. Shivashankar, S. Chandankumar. 2025-05-18. Arithmetic properties of $(\ell,m)$-regular colored partitions. https://arxiv.org/abs/2505.12270

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