Joint equidistributions of mesh patterns 123 and 132 with minus antipodal shadings

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-09-19 DOI:10.1016/j.dam.2025.09.002

Shuzhen Lv, Philip B. Zhang

引用次数: 0

Abstract

The study of joint equidistributions of mesh patterns 123 and 132 with the same symmetric shadings was recently initiated by Kitaev and Lv, where 75 of 80 potential joint equidistributions were proven. In this paper, we prove 112 out of 126 potential joint equidistributions of mesh patterns 123 and 132 with the same minus antipodal shadings. As a byproduct, we present 562 joint equidistribution results for non-symmetric and non-minus-antipodal shadings. To achieve this, we construct bijections, find recurrence relations, and obtain generating functions. Moreover, we demonstrate that the joint distributions of several pairs of mesh patterns are related to the unsigned Stirling numbers of the first kind.

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带负对映阴影的网格模式123和132的联合均匀分布

Kitaev和Lv最近开始了具有相同对称阴影的网格模式123和132的联合均匀分布的研究，其中80个潜在的联合均匀分布中有75个得到了证明。在本文中，我们证明了具有相同负对映阴影的网格模式123和132的126个潜在联合均匀分布中的112个。作为副产物，我们给出了562个非对称和非负对映投影的联合均匀分布结果。为了达到这个目的，我们构造双射，找到递归关系，并获得生成函数。此外，我们还证明了几对网格模式的联合分布与第一类无符号斯特林数有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.