We consider three notions of connectivity and their interactions in partially ordered sets coming from reduced factorizations of an element in a generated group. While one form of connectivity essentially reflects the connectivity of the poset diagram, the other two are a bit more involved: Hurwitz-connectivity has its origins in algebraic geometry, and shellability in topology. We propose a framework to study these connectivity properties in a uniform way. Our main tool is a certain linear order of the generators that is compatible with the chosen element.

中文翻译：

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生成群中分解位姿的连通性

我们考虑了连接性的三个概念及其在部分有序集合中的相互作用，这些概念来自生成组中元素的简化因式分解。虽然一种形式的连通性本质上反映了偏集图的连通性，但另外两种形式更复杂：Hurwitz 连通性起源于代数几何，而可壳性起源于拓扑。我们提出了一个框架来以统一的方式研究这些连接特性。我们的主要工具是与所选元素兼容的生成器的特定线性顺序。