论文标题
用避开图案的机器对凯利排列进行排序
Sorting Cayley permutations with pattern-avoiding machines
论文作者
论文摘要
克莱森（Claesson），法拉利（Ferrari）和现任作者最近引入了避开机器的模式，以更好地了解经典的$ 2 $ stacksort问题。在本文中，我们通过允许重复元素（也称为Cayley排列）的排列来概括这些设备。主要结果是对这些模式的描述，使得相应的排序排列集是类。我们还在Cayley排列的集合中展示了新的互动，该置换是通过作为操作员作为避免模式的堆栈而获得的。最后，我们分析了对Cayley排列的流行堆栈分类的两个概括。在这两种情况下，我们都在避免模式方面描述了可排序的排列。
Pattern avoiding machines were recently introduced by Claesson, Ferrari and the current author to gain a better understanding of the classical $2$-stacksort problem. In this paper we generalize these devices by allowing permutations with repeated elements, also known as Cayley permutations. The main result is a description of those patterns such that the corresponding set of sortable permutations is a class. We also show a new involution on the set of Cayley permutations, obtained by regarding a pattern-avoiding stack as an operator. Finally, we analyze two generalizations of pop-stack sorting on Cayley permutations. In both cases we describe sortable permutations in terms of pattern avoidance.
