计算作为集合的扁平分区产生的排列中的子词模式

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2022-01-01 DOI:10.2298/aadm210223009m

T. Mansour, M. Shattuck

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引用次数: 0

摘要

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。

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Counting subword patterns in permutations arising as flattened partitions of sets

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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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).