Harmonic numbers, Catalan's triangle and mesh patterns

Sergey Kitaev, Jeff Liese

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1515-1531
Number of pages17
JournalDiscrete Mathematics
Issue number14
Early online date16 Apr 2013
Publication statusPublished - 28 Jul 2013


  • mesh patterns
  • distribution
  • harmonic numbers
  • Catalan's triangle
  • generalized Stirling numbers
  • bijection


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