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

Fingerprint

Quadrant
Permutation
Mesh
Generating Function
Specialization
Continuation
Count

Keywords

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

Cite this

Kitaev, Sergey ; Remmel, Jeffrey ; Tiefenbruck, Mark. / Quadrant marked mesh patterns in 132-avoiding permutations. In: Pure Mathematics and Applications. 2012 ; Vol. 23, No. 3. pp. 219-256.
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Kitaev, S, Remmel, J & Tiefenbruck, M 2012, 'Quadrant marked mesh patterns in 132-avoiding permutations', Pure Mathematics and Applications, vol. 23, no. 3, pp. 219-256.

Quadrant marked mesh patterns in 132-avoiding permutations. / Kitaev, Sergey; Remmel, Jeffrey; Tiefenbruck, Mark.

In: Pure Mathematics and Applications, Vol. 23, No. 3, 2012, p. 219-256.

Research output: Contribution to journalArticle

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AU - Kitaev, Sergey

AU - Remmel, Jeffrey

AU - Tiefenbruck, Mark

PY - 2012

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KW - marked mesh pattern

KW - distribution

KW - Catalan numbers

KW - Fibonacci numbers

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