Let $\mathcal{S}$ denote the set of integer partitions into parts that differ by at least 3, with the added constraint that no two consecutive multiples of 3 occur as parts. We derive trivariate generating functions of Andrews–Gordon type for partitions in $\mathcal{S}$ with both the number of parts and the number of even parts counted. In particular, we provide an analytic counterpart of Andrews' recent refinement of the Alladi–Schur theorem.

中文翻译：

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链接分区理想和 Alladi-Schur 定理

让$\mathcal{小号}$表示整数划分为至少相差 3 的部分的集合，并附加约束，即没有两个连续的 3 的倍数作为部分出现。我们推导出 Andrews-Gordon 类型的三元生成函数用于分区$\mathcal{小号}$计算零件的数量和偶数零件的数量。特别是，我们提供了 Andrews 最近对 Alladi-Schur 定理的改进的分析对应物。