Distributions of several infinite families of mesh patterns

Sergey Kitaev, Philip B. Zhang, Xutong Zhang

Research output: Contribution to journalArticle

Abstract

Brändén and Claesson introduced mesh patterns to provide explicit expansions for certain permutation statistics as linear combinations of (classical) permutation patterns. The first systematic study of avoidance of mesh patterns was conducted by Hilmarsson et al., while the first systematic study of the distribution of mesh patterns was conducted by the first two authors.
In this paper, we provide far-reaching generalizations for 8 known distribution results and 5 known avoidance results related to mesh patterns by giving distribution or avoidance formulas for certain infinite families of mesh patterns in terms of distribution or avoidance formulas for smaller patterns. Moreover, as a corollary to a general result, we find the distribution of one more mesh pattern of length 2.
Original languageEnglish
Number of pages27
JournalApplied Mathematics and Computation
Publication statusAccepted/In press - 16 Dec 2019

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Statistics
Mesh
Permutation Statistics
Family
Linear Combination
Corollary
Permutation

Keywords

  • mesh patterns
  • permutation patterns
  • linear combinations

Cite this

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Distributions of several infinite families of mesh patterns. / Kitaev, Sergey; Zhang, Philip B.; Zhang, Xutong.

In: Applied Mathematics and Computation, 16.12.2019.

Research output: Contribution to journalArticle

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AU - Kitaev, Sergey

AU - Zhang, Philip B.

AU - Zhang, Xutong

PY - 2019/12/16

Y1 - 2019/12/16

N2 - Brändén and Claesson introduced mesh patterns to provide explicit expansions for certain permutation statistics as linear combinations of (classical) permutation patterns. The first systematic study of avoidance of mesh patterns was conducted by Hilmarsson et al., while the first systematic study of the distribution of mesh patterns was conducted by the first two authors. In this paper, we provide far-reaching generalizations for 8 known distribution results and 5 known avoidance results related to mesh patterns by giving distribution or avoidance formulas for certain infinite families of mesh patterns in terms of distribution or avoidance formulas for smaller patterns. Moreover, as a corollary to a general result, we find the distribution of one more mesh pattern of length 2.

AB - Brändén and Claesson introduced mesh patterns to provide explicit expansions for certain permutation statistics as linear combinations of (classical) permutation patterns. The first systematic study of avoidance of mesh patterns was conducted by Hilmarsson et al., while the first systematic study of the distribution of mesh patterns was conducted by the first two authors. In this paper, we provide far-reaching generalizations for 8 known distribution results and 5 known avoidance results related to mesh patterns by giving distribution or avoidance formulas for certain infinite families of mesh patterns in terms of distribution or avoidance formulas for smaller patterns. Moreover, as a corollary to a general result, we find the distribution of one more mesh pattern of length 2.

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KW - permutation patterns

KW - linear combinations

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JO - Applied Mathematics and Computation

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SN - 0096-3003

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