卷积序列，II：参数化
Convolutive sequences, II: Parametrizations
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中文总结 AI 辅助
该论文针对卷积序列研究，以参数化方法统一了除一个实例外的多数新发现的卷积eta积实例，完善了卷积序列的相关理论。
中文摘要 AI 辅助
在近期研究中，作者定义序列$(a_n)_{n\ge0}$为$m$阶卷积序列当且仅当对特定正整数$m$，满足$\sum_{n\ge0}a_{mn}q^n = \left(\sum_{n\ge0}a_n q^n\right)^m$，并证明了少量由本原eta积产生的序列的2阶和3阶卷积性。完成该工作后，作者发现了大量新的卷积eta积实例，本工作的核心是通过参数化方法统一其中除一个实例外的所有实例。
英文摘要
In recent work, the authors defined a sequence $(a_n)_{n\ge 0}$ to be $m$-convolutive exactly if \begin{align*} \sum_{n\ge 0} a_{mn} q^n = \left(\sum_{n\ge 0} a_n q^n\right)^m \end{align*} for a specific positive integer $m$ and provided proofs of the $2$- and $3$-convolutivity of a small number of sequences arising from primitive eta-products. Since the completion of that work, the authors have discovered many new instances of convolutive eta-products. The main focus of this work is to unify all but one of these instances in a parametric way.
