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Quadrant marked mesh patterns in 132-avoiding permutations

Kitaev, Sergey and Remmel, Jeffrey and Tiefenbruck, Mark (2012) Quadrant marked mesh patterns in 132-avoiding permutations. Pure Mathematics and Applications, 23 (3). pp. 219-256. ISSN 1218-4586

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Abstract

This paper is a continuation of the systematic study of the distributions of simple marked mesh patterns initiated in [6]. We study simple marked mesh patterns on 132-avoiding permutations. We derive generating functions for the number of occurrences of 4-parameter simple marked mesh patterns where only one parameter is allowed to be non-zero or a non-empty set. We show that specializations of such generating functions count a number of classical combinatorial sequences. Generating functions for the number of occurrences of 4-parameter simple marked mesh patterns where two or more of the parameters are allowed to be non-zero are studied in the upcoming paper [7].

Item type: Article
ID code: 49894
Keywords: permutation statistics, marked mesh pattern, distribution, Catalan numbers, Fibonacci numbers, Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Computer and Information Sciences
Depositing user: Pure Administrator
Date deposited: 17 Oct 2014 14:54
Last modified: 21 Oct 2018 00:35
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URI: https://strathprints.strath.ac.uk/id/eprint/49894
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