Bijections on pattern avoiding inversion sequences and related objects

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-09-04 DOI:10.1016/j.aam.2024.102771

JiSun Huh , Sangwook Kim , Seunghyun Seo , Heesung Shin

引用次数: 0

Abstract

The number of inversion sequences avoiding two patterns 101 and 102 is known to be the same as the number of permutations avoiding three patterns 2341, 2431, and 3241. This sequence also counts the number of Schröder paths without triple descents, restricted bicolored Dyck paths, $(101, 021)$ -avoiding inversion sequences, and weighted ordered trees. We provide bijections to integrate them together by introducing F-paths. Moreover, we define three kinds of statistics for each of the objects and count the number of each object with respect to these statistics. We also discuss direct sums of each object.

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避免反转序列和相关对象的模式双射

已知避免 101 和 102 两种模式的反转序列数与避免 2341、2431 和 3241 三种模式的排列数相同。这个序列还计算了没有三重下降的施罗德路径、受限双色戴克路径、避免 (101,021) 反转序列和加权有序树的数量。通过引入 F 路径，我们提供了将它们整合在一起的双射。此外，我们还为每个对象定义了三种统计量，并计算了与这些统计量相关的每个对象的数量。我们还讨论了每个对象的直接和。

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

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.