论文标题
在比赛和参与中避免模式
On pattern avoidance in matchings and involutions
论文作者
论文摘要
我们研究了对称群体中的两种模式避免概念的关系，以及它们限制对无定点的互动的限制。第一个是经典的，而第二个是在某些球形品种的几何形状中出现的，并概括了jelínek研究的完美匹配的图案避免概念。第一个概念始终可以用第二个概念来表示，我们给出了有效的算法。我们还给出了部分结果，描述了匡威所拥有的互动家族。结果，我们证明了麦戈文的两种猜想，这些猜想是某些品种的（理性）平滑度的表征。我们还提供了新的列举结果，并通过提出几条询问线来扩展我们当前的工作。
We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain spherical varieties and generalizes the notion of pattern avoidance for perfect matchings studied by Jelínek. The first notion can always be expressed in terms of the second, and we give an effective algorithm to do so. We also give partial results characterizing the families of involutions where the converse holds. As a consequence, we prove two conjectures of McGovern characterizing (rational) smoothness of certain varieties. We also give new enumerative results, and conclude by proposing several lines of inquiry that extend our current work.
