Abstract

Permutations that can be sorted greedily by one or more stacks having various constraints have been studied by a number of authors. A pop-stack is a greedy stack that must empty all entries whenever popped. Permutations in the image of the pop-stack operator are said to be pop-stacked. Asinowki, Banderier, Billey, Hackl, and Linusson recently investigated these permutations and calculated their number up to length 16. We give a polynomial-time algorithm to count pop-stacked permutations up to a fixed length and we use it to compute the first 1000 terms of the corresponding counting sequence. With the 1000 terms, we apply a pair of computational methods to prove some negative results concerning the nature of the generating function for pop-stacked permutations and to empirically predict the asymptotic behavior of the counting sequence using differential approximation.

摘要

许多作者研究了可以通过具有各种约束的一个或多个堆栈进行贪婪排序的排列。弹出堆栈是一个贪婪的堆栈，每当弹出时都必须清空所有条目。pop-stack 运算符图像中的排列被称为pop-stacked. Asinowki、Banderier、Billey、Hackl 和 Linusson 最近研究了这些排列并计算了它们的数量，最大长度为 16。我们给出了一个多项式时间算法来计算弹出堆叠排列的最大固定长度，我们用它来计算前 1000 个相应计数序列的术语。对于 1000 项，我们应用一对计算方法来证明关于弹出堆叠排列的生成函数的性质的一些负面结果，并使用微分逼近根据经验预测计数序列的渐近行为。