Modular Forms and $k$-colored Generalized Frobenius Partitions

Heng Huat Chan; Liuquan Wang; Yifan Yang

Modular Forms and $k$-colored Generalized Frobenius Partitions

Number Theory 2021-06-02 v2 Combinatorics

Authors: Heng Huat Chan , Liuquan Wang , Yifan Yang

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 $\mathrm{C}\Phi_k(q)$ .

Keywords

modular forms partition congruences partition theory

Cite

@article{arxiv.1706.03020,
  title  = {Modular Forms and $k$-colored Generalized Frobenius Partitions},
  author = {Heng Huat Chan and Liuquan Wang and Yifan Yang},
  journal= {arXiv preprint arXiv:1706.03020},
  year   = {2021}
}

Comments

46 pages. We added a section of corrigendum on the last page, which corrects several typos in the published version

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