AI 中文总结
研究涉及超分割和最小排除数的双色分拆恒等式，通过构造显式保权双射和奇偶反转对合给出组合证明，还给出相关超分割精细化的新组合证明。
AI 中文摘要
Andrews和El Bachraoui研究了偶数部分仅以蓝色出现的双色分拆，得到了这些分拆的奇偶精细化与超分割和最小排除数相关的几个恒等式。他们的一些证明是解析的，依赖于q - 级数操作。本文构造了显式保权双射和奇偶反转对合，为这些恒等式提供组合证明。我们还给出了涉及\(\overline{p}(n)\)和\(\overline{p}_o(n)\)的相关超分割精细化的新组合证明。
英文摘要
Andrews and El Bachraoui investigated two-color partitions in which even parts may occur only in blue and obtained several identities relating parity refinements of these partitions to overpartitions and minimal excludants. Some of their proofs are analytic and rely on $q$-series manipulations. In this paper, we construct explicit weight-preserving bijections and parity-reversing involutions that provide combinatorial proofs of these identities. We also give a new combinatorial proof of related overpartition refinements involving $\overline{p}(n)$ and $\overline{p}_o(n)$.
