For a composition λ of n we consider the Kazhdan–Lusztig cell in the symmetric group Sn containing the longest element of the standard parabolic subgroup of Sn associated to λ. In this paper, we extend some of the ideas and results in [Beiträge zur Algebra und Geometrie, 59(3) (2018) 523–547]. In particular, by introducing the notion of an ordered k-path, we are able to obtain alternative explicit descriptions for some additional families of cells associated to compositions. This is achieved by first determining the rim of the cell, from which reduced forms for all the elements of the cell are easily obtained.

中文翻译：

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关于 Sn 的某些 Kazhdan-Lusztig 细胞家族的有序 k 路径和边缘

对于一个组合λ的n我们考虑对称群中的 Kazhdan-Lusztig 单元小号n包含的标准抛物子群的最长元素小号n关联到λ. 在本文中，我们将一些想法和结果扩展到 [Beiträge zur 代数和几何,59(3) (2018) 523–547]。特别是，通过引入有序的概念ķ-path，我们能够获得与组合相关的一些额外的细胞家族的替代明确描述。这是通过首先确定单元的边缘来实现的，从中可以很容易地获得单元的所有元素的简化形式。