### Abstract

Original language | English |
---|---|

Pages (from-to) | 219-256 |

Number of pages | 38 |

Journal | Pure Mathematics and Applications |

Volume | 23 |

Issue number | 3 |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

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

### Cite this

*Pure Mathematics and Applications*,

*23*(3), 219-256.

}

*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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quadrant marked mesh patterns in 132-avoiding permutations

AU - Kitaev, Sergey

AU - Remmel, Jeffrey

AU - Tiefenbruck, Mark

PY - 2012

Y1 - 2012

N2 - 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].

AB - 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].

KW - permutation statistics

KW - marked mesh pattern

KW - distribution

KW - Catalan numbers

KW - Fibonacci numbers

UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/newMM132-I.pdf

UR - http://puma.dimai.unifi.it/23_3.php

M3 - Article

VL - 23

SP - 219

EP - 256

JO - Pure Mathematics and Applications

JF - Pure Mathematics and Applications

SN - 1218-4586

IS - 3

ER -