### Abstract

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 language | English |
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Number of pages | 27 |

Journal | Applied Mathematics and Computation |

Publication status | Accepted/In press - 16 Dec 2019 |

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### Keywords

- mesh patterns
- permutation patterns
- linear combinations

### Cite this

*Applied Mathematics and Computation*.

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*Applied Mathematics and Computation*.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Distributions of several infinite families of mesh patterns

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.

KW - mesh patterns

KW - permutation patterns

KW - linear combinations

UR - https://www.sciencedirect.com/journal/applied-mathematics-and-computation

M3 - Article

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -