阶梯图、模式避免与光滑置换
Staircase diagrams, pattern avoidance, and smooth permutations
浏览论文内容
中文总结 AI 辅助
本文研究阶梯图偏序结构与光滑置换模式避免的联系，并枚举了包括抛光置换在内的若干光滑置换子类。
中文摘要 AI 辅助
Lakshmibai 和 Sandhya 的一个著名结果表明，A 型光滑 Schubert 簇对应于避免模式 3412 和 4231 的置换。后来，第二作者与 Slofstra 证明了，在简单连通 Dynkin 图上的阶梯图与相应类型的光滑 Schubert 簇之间存在双射。我们探讨阶梯图的偏序集结构如何与光滑置换上的模式避免相关联。作为应用，我们枚举了若干由模式避免刻画的光滑置换子类。这些子类包括由 Gaetz 和 Gao 研究过的抛光置换类。
英文摘要
A well known result due to Lakshmibai and Sandhya states that smooth Schubert varieties of type A correspond to permutations that avoid the patterns 3412 and 4231. It was later shown by the second author and Slofstra that staircase diagrams over a simply-laced Dynkin diagram are in bijection with smooth Schubert varieties of the corresponding type. We explore how the poset structure of staircase diagrams is connected with pattern avoidance on smooth permutations. As an application, we enumerate several subclasses of smooth permutations which are characterized by pattern avoidance. These subclasses include the class of polished permutations which were studied by Gaetz and Gao.
发表机构
- Lewis-Clark State College（路易斯-克拉克州立学院）
- Oklahoma State University（俄克拉荷马州立大学）
机构由 AI 辅助整理，请以论文原文为准。
