Quadrant marked mesh patterns in 132-avoiding permutations

Sergey Kitaev, Jeffrey Remmel, Mark Tiefenbruck

Research output: Contribution to journalArticle

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].
Original languageEnglish
Pages (from-to)219-256
Number of pages38
JournalPure Mathematics and Applications
Volume23
Issue number3
Publication statusPublished - 2012

Keywords

  • permutation statistics
  • marked mesh pattern
  • distribution
  • Catalan numbers
  • Fibonacci numbers

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