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arXiv · 2510.19242

Congruences modulo powers of $3$ for generalized Frobenius partitions $C\Psi_{6,0}$

Dandan Chen·Siyu Yin
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Abstract

In 1984, Andrews introduced the family of partition functions \(c\phi_k(n)\), which counts the number of generalized Frobenius partitions of \(n\) with \(k\) colors. In previous work, we proved a conjecture on congruences for \(c\phi_6(n)\) modulo powers of 3. In this paper, we consider the \((6,0)\)-colored Frobenius partition functions \(c\psi_{6,0}(n)\). We establish a connection between the generating functions of \(c\psi_{6,3}(n)\) and \(c\psi_{6,0}(n)\) via an Atkin-Lehner involution, and prove congruences modulo powers of 3 for \(c\psi_{6,0}(n)\).

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Dandan Chen, Siyu Yin. 2025-10-22. Congruences modulo powers of $3$ for generalized Frobenius partitions $C\Psi_{6,0}$. https://arxiv.org/abs/2510.19242

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