Congruences modulo powers of 3 for generalized Frobenius partitions C6,0
Abstract
In 1984, Andrews introduced the family of partition functions \(cφk(n)\), which counts the number of generalized Frobenius partitions of \(n\) with \(k\) colors. In previous work, we proved a conjecture on congruences for \(cφ6(n)\) modulo powers of 3. In this paper, we consider the \((6,0)\)-colored Frobenius partition functions \(c6,0(n)\). We establish a connection between the generating functions of \(c6,3(n)\) and \(c6,0(n)\) via an Atkin-Lehner involution, and prove congruences modulo powers of 3 for \(c6,0(n)\).
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