Modular forms and 𝑘-colored generalized Frobenius partitions

Chan, Heng Huat; Wang, Liuquan; Yang, Yifan

doi:10.1090/tran/7447

Modular forms and $k$-colored generalized Frobenius partitions
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by Heng Huat Chan, Liuquan Wang and Yifan Yang PDF

Trans. Amer. Math. Soc. 371 (2019), 2159-2205 Request permission

Abstract:

Let $k$ and $n$ be positive integers. Let $c\phi _{k}(n)$ denote the number of $k$-colored generalized Frobenius partitions of $n$ and let $\mathrm {C}\Phi _k(q)$ be the generating function of $c\phi _{k}(n)$. In this article, we study $\mathrm {C}\Phi _k(q)$ using the theory of modular forms and discover new surprising properties of $\mathrm {C}\Phi _k(q)$.

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