Modular Forms and $k$-colored Generalized Frobenius Partitions

Heng Huat Chan; Liuquan Wang; Yifan Yang

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arXiv · 1706.03020

Modular Forms and $k$-colored Generalized Frobenius Partitions

Heng Huat Chan·Liuquan Wang·Yifan Yang

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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 $\mathrm{C}\Phi_k(q)$ 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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Heng Huat Chan, Liuquan Wang, Yifan Yang. 2017-06-09. Modular Forms and $k$-colored Generalized Frobenius Partitions. https://arxiv.org/abs/1706.03020

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