偏序集$Q$的$-Q$是什么？
What is $-Q$ for a poset $Q$?
摘要：
在组合互易性的上下文中，问偏序集$Q$的“$-Q$“是什么是一个自然的问题。基于半代数集的欧拉示性数的概念，提出了“具有字典序的$-Q:=Q\times\mathbb{R}$”的定义.实际上，利用这个定义，Stanley关于阶多项式的互易性被推广为偏序集之间的某些增映射空间的欧拉示性数的等式。本文的目的是改进这一结果，即证明如果$Q$的拓扑是可度量化的，则这些空间是同胚的。
英文摘要：
In the context of combinatorial reciprocity, it is a natural question to ask what "$-Q$" is for a poset $Q$. In a previous work, the definition "$-Q:=Q\times\mathbb{R}$ with lexicographic order" was proposed based on the notion of Euler characteristic of semialgebraic sets. In fact, by using this definition, Stanley's reciprocity for order polynomials was generalized to an equality for the Euler characteristics of certain spaces of increasing maps between posets. The purpose of this paper is to refine this result, that is, to show that these spaces are homeomorphic if the topology of $Q$ is metrizable.
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。
