论文标题
步行的矢量内核法更长
The vectorial kernel method for walks with longer steps
论文作者
论文摘要
Asinowski，Bacher，Banderier和Gitterberger（A.Asinowski，A。Bacher，C。Banderier和B. Gittenberger。晶格路径的分析组合学具有禁止模式的分析组合，矢量核方法，矢量核方法，以及为推送自动化的功能生成algoritha。Algoritha。经典内核方法可用于遵守有限自动机可以描述的路径，例如避免使用固定的图案，一次避免使用几种模式，停留在水平条中，以及更多其他图案。但是，他们仅考虑步行为一步。在本文中，我们将其结果推广到步行较长的步行。我们还将给出此扩展的一些应用，并证明有关Schroeder路径中预期数量上升数的渐近行为的猜想。
Asinowski, Bacher, Banderier and Gittenberger (A. Asinowski, A. Bacher, C. Banderier and B. Gittenberger. Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata. Algorithmica, pp. 1-43, 2019.) recently developed the vectorial kernel method - a powerful extension of the classical kernel method that can be used for paths that obey constraints that can be described by finite automata, e.g. avoid a fixed pattern, avoid several patterns at once, stay in a horizontal strip and many others more. However, they only considered walks with steps of length one. In this paper we will generalize their results to walks with longer steps. We will also give some applications of this extension and prove a conjecture about the asymptotic behavior of the expected number of ascents in Schroeder paths.
