论文标题
流行，裂纹，快照（和战俘）：碎片的一些方面
Pop, Crackle, Snap (and Pow): Some Facets of Shards
论文作者
论文摘要
阅读将超中央布置中的超平面削减了$ \ mathcal h $的碎片，称为\ emph {shards}，反映了安排的顺序理论属性。我们表明，碎片具有自然的解释，是$ \ Mathcal H $综合的基本组的某些发电机。仅在这些发电机中呈正表情产生一个新的poset，我们称之为\ emph {pure shard monoid}。 当$ \ Mathcal H $很简单时，它的区域是一个晶格，因此它配备了Pop-stack-STACK STACTing Operator $ \ Mathsf {pop} $。在这种情况下，我们使用$ \ mathsf {pop} $来定义阅读碎片的交叉点的嵌入$ \ mathsf {crackle} $中的纯shard monoid。当$ \ Mathcal H $是有限的Coxeter组的反射安排时，我们还定义了shard交叉点的$ \ mathsf {snap} $的poset嵌入到正辫中；在这种情况下，我们的三个地图与$ \ Mathsf {snap} = \ mathsf {crackle} \ cdot \ mathsf {pop} $相关。
Reading cut the hyperplanes in a real central arrangement $\mathcal H$ into pieces called \emph{shards}, which reflect order-theoretic properties of the arrangement. We show that shards have a natural interpretation as certain generators of the fundamental group of the complement of the complexification of $\mathcal H$. Taking only positive expressions in these generators yields a new poset that we call the \emph{pure shard monoid}. When $\mathcal H$ is simplicial, its poset of regions is a lattice, so it comes equipped with a pop-stack sorting operator $\mathsf{Pop}$. In this case, we use $\mathsf{Pop}$ to define an embedding $\mathsf{Crackle}$ of Reading's shard intersection order into the pure shard monoid. When $\mathcal H$ is the reflection arrangement of a finite Coxeter group, we also define a poset embedding $\mathsf{Snap}$ of the shard intersection order into the positive braid monoid; in this case, our three maps are related by $\mathsf{Snap}=\mathsf{Crackle} \cdot \mathsf{Pop}$.
