Harmonic numbers, Catalan's triangle and mesh patterns

Kitaev, Sergey and Liese, Jeff (2013) Harmonic numbers, Catalan's triangle and mesh patterns. Discrete Mathematics, 313 (14). pp. 1515-1531. ISSN 0012-365X (https://doi.org/10.1016/j.disc.2013.03.017)

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Abstract

The notion of a mesh pattern was introduced recently, but it has already proved to be a useful tool for description purposes related to sets of permutations. In this paper we study eight mesh patterns of small lengths. In particular, we link avoidance of one of the patterns to the harmonic numbers, while for three other patterns we show their distributions on 132-avoiding permutations are given by the Catalan triangle. Also, we show that two specific mesh patterns are Wilf-equivalent. As a byproduct of our studies, we define a new set of sequences counted by the Catalan numbers and provide a relation on the Catalan triangle that seems to be new.

ORCID iDs

Kitaev, Sergey ORCID logoORCID: https://orcid.org/0000-0003-3324-1647 and Liese, Jeff;
  • Item type:Article
    ID code:49884
    Dates:
    Date
    Event
    28 July 2013
    Published
    16 April 2013
    Published Online
    Keywords:mesh patterns, distribution, harmonic numbers, Catalan's triangle, generalized Stirling numbers, bijection, Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Theoretical Computer Science
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:17 Oct 2014 10:48
    Last modified:29 Jan 2021 04:37
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/49884
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