What is -Q for a poset Q?
What is -Q for a poset Q?
复制标题
什么是偏序集 Q 的 -Q？
DOI：
10.1007/s11083-022-09600-y
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发表时间：
2022
期刊：
影响因子：
0.4
通讯作者：
Yoshinaga Masahiko
中科院分区：
文献类型：
--
作者：
Yoshida Taiga;Yoshinaga Masahiko
在组合互易性的背景下，很自然地会问“”对于posetQ来说是什么。在前人的工作中，基于半代数集的欧拉特征的概念，提出了“有词典序”的定义。实际上，利用这个定义，Stanley关于序多项式的倒易性被推广到偏序集之间递增映射的某些空间的Euler特征相等。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。
In the context of combinatorial reciprocity, it is a natural question to ask what “” is for a posetQ. In a previous work, the definition “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 ofQis metrizable.