Congruences modulo powers of $3$ for generalized Frobenius partitions $CΨ_{6,0}$

Dandan Chen; Siyu Yin

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arXiv · 2510.19242

Congruences modulo powers of $3$ for generalized Frobenius partitions $CΨ_{6,0}$

Dandan Chen·Siyu Yin

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Abstract

In 1984, Andrews introduced the family of partition functions $cϕ_k(n)$, which counts the number of generalized Frobenius partitions of $n$ with $k$ colors. In previous work, we proved a conjecture on congruences for $cϕ_6(n)$ modulo powers of 3. In this paper, we consider the $(6,0)$-colored Frobenius partition functions $cψ_{6,0}(n)$. We establish a connection between the generating functions of $cψ_{6,3}(n)$ and $cψ_{6,0}(n)$ via an Atkin-Lehner involution, and prove congruences modulo powers of 3 for $cψ_{6,0}(n)$.

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BibTeX RIS

Dandan Chen, Siyu Yin. 2026-04-16. Congruences modulo powers of $3$ for generalized Frobenius partitions $CΨ_{6,0}$. https://arxiv.org/abs/2510.19242

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