Pattern-restricted permutations of small order

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-05-16 DOI:10.1016/j.disc.2025.114566

Kassie Archer, Robert P. Laudone

引用次数: 0

Abstract

In this paper, we develop a framework for studying pattern avoidance in permutations composed of small cycles via Dyck words, arc diagrams and free blocks. We then apply this to enumerate 132-avoiding permutations of order 3 in terms of the Catalan and Motzkin generating functions, answering a question of Bóna and Smith from 2019. We also enumerate 231-avoiding permutations that are composed only of 3-cycles, 2-cycles, and fixed points.

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小顺序的模式限制排列

在本文中，我们开发了一个框架来研究由Dyck词、圆弧图和自由块组成的小循环排列中的模式避免。然后，我们将其应用于根据Catalan和Motzkin生成函数枚举3阶的132避免排列，回答Bóna和Smith从2019年提出的问题。我们还列举了仅由3环、2环和不动点组成的231避免排列。

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 Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.