English

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

Combinatorics 2025-05-20 v1 Number Theory

Abstract

Let b,mk(n)b^{k}_{\ell,m}(n) denotes the number of kk-colored partitions of nn into parts that are not multiples of \ell or mm. We establish several congruence relations for b,m(n)b_{\ell,m}(n). For instance, for any nonnegative integer nn b4,52(8n+7)0(mod40).b^{2}_{4,5}(8n+7) \equiv 0 \pmod{40}.

Keywords

Cite

@article{arxiv.2505.12270,
  title  = {Arithmetic properties of $(\ell,m)$-regular colored partitions},
  author = {Yashas N. and C. Shivashankar and S. Chandankumar},
  journal= {arXiv preprint arXiv:2505.12270},
  year   = {2025}
}
R2 v1 2026-07-01T02:19:17.118Z