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arXiv · 2504.04983

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

Dandan Chen·Siyu Yin
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Abstract

In $1984$, Andrews introduced the family of partition functions $cϕ_k(n)$, which enumerate generalized Frobenius partitions of $n$ with $k$ colors. In $2016$, Gu, Wang, and Xia established several congruences for $cϕ_6(n)$ 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.

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Dandan Chen, Siyu Yin. 2026-04-05. Congruences modulo powers of $3$ for $6$-colored generalized Frobenius partitions. https://arxiv.org/abs/2504.04983

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