关于偶部低于奇部的分拆和余分拆的无穷乘积的正性
On the positivity of infinite products connected to partitions with even parts below odd parts and copartitions
摘要：
本文给出了与Andrews的$\mathcal{EO}^*$型划分有关的Chern的一个正性结果的组合证明.这个组合证明是在重新构造陈省身的结果后得到的。利用这个新的视角，我们还重新证明了陈省身的一个超分割结果，证明了它本质上是“免费的”，从我们的组合证明和一些基本性质的copartition。最后，应用copartition导致我们更普遍的正性的家庭的无限和有限的产品，证明在一个特殊的情况下。
英文摘要：
In this paper, we give a combinatorial proof of a positivity result of Chern related to Andrews's $\mathcal{EO}^*$-type partitions. This combinatorial proof comes after reframing Chern's result in terms of copartitions. Using this new perspective, we also reprove an overpartition result of Chern by showing that it comes essentially "for free" from our combinatorial proof and some basic properties of copartitions. Finally, the application of copartitions leads us to more general positivity conjectures for families of both infinite and finite products, with a proof in one special case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
