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

D. S. Gireesh; HemanthKumar B

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

Number Theory 2025-03-06 v1

Authors: D. S. Gireesh , HemanthKumar B

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.

Keywords

partition congruences partition theory ramanujan identities and series

Cite

@article{arxiv.2503.02366,
  title  = {On $7^k$-regular partitions modulo powers of $7$},
  author = {D. S. Gireesh and HemanthKumar B},
  journal= {arXiv preprint arXiv:2503.02366},
  year   = {2025}
}

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