Abstract Recently, Beck posed two conjectures on the difference between the number of (respectively, distinct) parts in the odd partitions of n and the number of (respectively, distinct) parts in the distinct partitions of n . These two conjectures were first confirmed by Andrews using generating functions, and then generalized by Fu and Tang, and Yang in different ways. Motivated by Yang’s work, we present two more generalized results and prove them both analytically and combinatorially.

中文翻译：

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George Beck的两个问题的概括

摘要 最近，贝克对 n 的奇数分区中的（分别不同的）部分的数量与 n 的不同分区中的（分别不同的）部分的数量之间的差异提出了两个猜想。这两个猜想首先被安德鲁斯使用生成函数证实，然后被傅、唐和杨以不同的方式推广。在杨的工作的推动下，我们提出了两个更普遍的结果，并通过分析和组合来证明它们。