Abstract
We present the generating function for \(c\phi _6(n)\), the number of generalized Frobenius partitions of \(n\) with \(6\) colors, in terms of Ramanujan’s theta functions and exhibit \(2\), and \(3\)-dissections of it that yield the congruences \(c\phi _6(2n+1)\equiv 0~(\text {mod}~4)\), \(c\phi _6(3n+1)\equiv 0~(\text {mod}~3^2)\) and \(c\phi _6(3n+2)\equiv 0~(\text {mod}~3^2)\).
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The authors are extremely grateful to the anonymous referee for his/her helpful suggestions.
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Baruah, N.D., Sarmah, B.K. Generalized Frobenius partitions with 6 colors. Ramanujan J 38, 361–382 (2015). https://doi.org/10.1007/s11139-014-9595-2
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DOI: https://doi.org/10.1007/s11139-014-9595-2