分拆中缺失整数个数相关的恒等式——组合证明
Identities involving the number of missing integers in partitions - combinatorial proofs
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中文总结 AI 辅助
针对Bhoria等人关于分拆中缺失整数个数的相关结果，本文提供了组合证明，丰富了分拆组合学领域的研究内容。
中文摘要 AI 辅助
分拆λ中的缺失整数是指小于λ的最大部分且未作为λ的部分出现的正整数。在近期论文《分拆中缺失整数的个数》中，Bhoria、Eyyunni和Santra研究了n的分拆（超分拆）中具有固定缺失整数个数的分拆数量，并建立了对应的生成函数、恒等式和同余式。在本文中，我们为他们的若干结果提供了组合证明。
英文摘要
A missing integer in a partition $λ$ is a positive integer less than the largest part of $λ$ that does not appear as a part in $λ$. In the recent paper On the number of missing integers in partitions, Bhoria, Eyyunni, and Santra examined the number of partitions (overpartitions) of $n$ with a fixed number of missing integers and established generating functions, identities, and congruences for them. In this article, we provide combinatorial proofs for several of their results.
