Quadrant marked mesh patterns

Sergey Kitaev, Jeffrey Remmel

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper we begin the first systematic study of distributions of quadrant marked mesh patterns. Mesh patterns were introduced recently by Brändén and Claesson in connection with permutation statistics. Quadrant marked mesh patterns are based on how many elements lie in various quadrants of the graph of a permutation relative to the coordinate system centered at one of the points in the graph of the permutation. We study the distribution of several quadrant marked mesh patterns in a symmetric group and in certain subsets of the symmetric group. We find explicit formulas for the generating function of such distributions in several general cases and develop recursions to compute the numbers in question in other cases. In addition, certain q-analogues of our results are discussed.
Original languageEnglish
Article number12.4.7
Number of pages29
JournalJournal of Integer Sequences
Volume15
Issue number4
Publication statusPublished - 2012

Keywords

  • quadrant marked mesh patterns
  • mesh patterns
  • permutation

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