### Abstract

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

Article number | 12.4.7 |

Number of pages | 29 |

Journal | Journal of Integer Sequences |

Volume | 15 |

Issue number | 4 |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- quadrant marked mesh patterns
- mesh patterns
- permutation

### Cite this

*Journal of Integer Sequences*,

*15*(4), [12.4.7].

}

*Journal of Integer Sequences*, vol. 15, no. 4, 12.4.7.

**Quadrant marked mesh patterns.** / Kitaev, Sergey; Remmel, Jeffrey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quadrant marked mesh patterns

AU - Kitaev, Sergey

AU - Remmel, Jeffrey

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - quadrant marked mesh patterns

KW - mesh patterns

KW - permutation

UR - https://cs.uwaterloo.ca/journals/JIS/VOL15/Kitaev/kitaev5.pdf

UR - https://cs.uwaterloo.ca/journals/JIS/VOL15/Kitaev/kitaev5.html

M3 - Article

VL - 15

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

SN - 1530-7638

IS - 4

M1 - 12.4.7

ER -