Pattern-avoiding stabilized-interval-free permutations

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-11-19 DOI:10.1016/j.disc.2024.114329

Daniel Birmajer , Juan B. Gil , Jordan O. Tirrell , Michael D. Weiner

引用次数: 0

Abstract

In this paper, we study pattern avoidance for stabilized-interval-free (SIF) permutations. These permutations are contained in the set of indecomposable permutations and in the set of derangements. We enumerate pattern-avoiding SIF permutations for classical and pairs of patterns of size 3. In particular, for the patterns 123 and 231, we rely on combinatorial arguments and the fixed-point distribution of general permutations avoiding these patterns. We briefly discuss 123-avoiding permutations with two fixed points and offer a conjecture for their enumeration by the distance between their fixed points. For the pattern 231, we also give a direct argument that uses a bijection to ordered forests.

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图案规避稳定无间隔排列

本文研究了无稳定间隔（SIF）排列的模式规避问题。这些排列包含在不可分解排列集合和变形集合中。我们列举了经典模式和大小为 3 的成对模式的避模式 SIF 置换。特别是对于 123 和 231 图案，我们依靠组合论证和避开这些图案的一般排列的定点分布。我们简要讨论了有两个定点的 123 回避排列，并提出了通过定点间的距离枚举它们的猜想。对于模式 231，我们还给出了一个使用有序森林双射的直接论证。

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.