Arithmetic Properties for $k$-Color Analogue of Simultaneously $s$-Regular and $t$-Distinct Partitions

Anjelin Mariya Johnson; S. N. Fathima

Arithmetic Properties for $k$-Color Analogue of Simultaneously $s$-Regular and $t$-Distinct Partitions

Combinatorics 2026-07-13 v1 Number Theory

Authors: Anjelin Mariya Johnson , S. N. Fathima

Abstract

In this article, we discuss general generating functions for partitions of $n$ , simultaneously $s$ -regular and $t$ -distinct in 3-colors. In addition, we obtain infinite families of congruences modulo powers of 3 for specific values of $(\ell,t)$ . For instance, for positive integers $n$ and $k$ , we have \begin{align*} \sum_{n=o}^{\infty}RD_3^{3,3}\left(3^kn+\frac{3^k+1}{2}\right)q^n\equiv0 \pmod{3^{k+1}}. \end{align*}

Keywords

partitions s-regular t-distinct congruences generating functions k-color

Cite

@article{arxiv.2607.11499,
  title  = {Arithmetic Properties for $k$-Color Analogue of Simultaneously $s$-Regular and $t$-Distinct Partitions},
  author = {Anjelin Mariya Johnson and S. N. Fathima},
  journal= {arXiv preprint arXiv:2607.11499},
  year   = {2026}
}