Kitaev, Sergey and Liese, Jeff (2013) Harmonic numbers, Catalan's triangle and mesh patterns. Discrete Mathematics, 313 (14). pp. 1515-1531. ISSN 0012-365XFull text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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:||22 Mar 2017 13:35|