Congruences modulo powers of $3$ for $6$-colored generalized Frobenius partitions

Abstract

In $1984$, Andrews introduced the family of partition functions $c{\varphi }_k(n)$, which enumerate generalized Frobenius partitions of $n$ with $k$ colors. In $2016$, Gu, Wang, and Xia established several congruences for $c{\varphi }_6(n)$ and proposed a conjecture concerning congruences modulo powers of $3$ for this function. In this paper, we resolve a revised version of their conjecture by employing an approach analogous to that developed by Banerjee and Smoot.

arXiv comment15 pages