带气孔的斜戴克路径

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-05-03 DOI:10.1007/s00010-024-01065-1

Jean-Luc Baril, Rémi Maréchal, Helmut Prodinger

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引用次数: 0

摘要

我们得出了 n 个长度的部分倾斜戴克气穴路径（DAP）中以给定序数为终点的数量的双变量生成函数。我们还给出了给定长度的所有部分偏斜戴克路径中端点平均序数的渐近近似值。我们还对两个偏斜 DAP 子类进行了类似研究，即避谷偏斜 DAP 和之字形、避谷偏斜 DAP。我们用瑞尔丹数组来表示这些结果。最后，我们提出了两个一一对应的二进制单词，它们避免了 00 和 0110 的模式，以及带有 \(\{2,1,3,5,7,\ldots \}\) 部分的宫位合成。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Skew Dyck paths with air pockets

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Skew Dyck paths with air pockets

We yield bivariate generating function for the number of n-length partial skew Dyck paths with air pockets (DAPs) ending at a given ordinate. We also give an asymptotic approximation for the average ordinate of the endpoint in all partial skew DAPs of a given length. Similar studies are made for two subclasses of skew DAPs, namely valley-avoiding and zigzagging, valley-avoiding skew DAPs. We express these results as Riordan arrays. Finally, we present two one-to-one correspondences with binary words avoiding the patterns 00 and 0110, and palindromic compositions with parts in \(\{2,1,3,5,7,\ldots \}\).

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.