Counting subword patterns in permutations arising as flattened partitions of sets

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.2298/aadm210223009m

T. Mansour, M. Shattuck

引用次数: 0

Abstract

We consider various statistics on the set Fn consisting of the distinct permutations of length n+1 that arise as a flattening of some partition of the same size. In particular, we enumerate members of Fn according to the number of occurrences of three-letter consecutive patterns, considered more broadly in the context of r-partitions. As special cases of our results, we obtain formulas for the number of members of Fn avoiding a given consecutive pattern and for the total number of occurrences of a pattern over all members of Fn.

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计算作为集合的扁平分区产生的排列中的子词模式

我们考虑由长度为n+1的不同排列组成的集合Fn上的各种统计量，这些排列是由一些相同大小的分区的平坦化产生的。特别是，我们根据三个字母连续模式的出现次数来枚举Fn的成员，在r分区的上下文中更广泛地考虑。作为我们的结果的特殊情况，我们得到Fn中避免给定连续模式的成员的数目和在Fn的所有成员中出现一个模式的总次数的公式。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.