Abstract

We investigate two truncated series derived recently by S. H. Chan, T. P. N. Ho, and R. Mao from the Watson quintuple product identity and experimentally discover two stronger results. In this context, for each $S\in \{1,2\}$, we obtain two infinite families of linear homogeneous inequalities for the number of partitions of n into parts congruent to $\pm S\mathrm{mod}5$.

中文翻译：

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关于两个截断的五元级数级数定理

摘要

我们调查了 SH Chan、TPN Ho 和 R. Mao 最近从 Watson 五元组产品标识中推导出的两个截断系列，并通过实验发现了两个更强的结果。在这种情况下，对于每个$\mathrm{小号}\in \{1,2\}$，我们获得了两个无限的线性齐次不等式族，它们将n的分区数划分为相等的部分$\pm \mathrm{小号}\mathrm{模组}5$.