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arXiv · 2412.16193

Arithmetic properties of $k$-tuple $\ell$-regular partitions

Hemjyoti Nath·Manjil P. Saikia·Abhishek Sarma
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Abstract

In this paper, we study arithmetic properties satisfied by the $k$-tuple $\ell$-regular partitions. A $k$-tuple of partitions $(\xi_1, \xi_2, \ldots, \xi_k)$ is said to be $\ell$-regular if all the $\xi_i$'s are $\ell$-regular. We study the cases $(\ell, k)=(2,3), (4,3), (\ell, p)$, where $p$ is a prime, and even the general case when both $\ell$ and $k$ are unrestricted. Using elementary means as well as the theory of modular forms we prove several infinite family of congruences and density results for these family of partitions.

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Hemjyoti Nath, Manjil P. Saikia, Abhishek Sarma. 2024-12-16. Arithmetic properties of $k$-tuple $\ell$-regular partitions. https://arxiv.org/abs/2412.16193

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