### 摘要

Let C_{n} be the set of Dyck paths of length n. In this paper, by a new auto- morphism of ordered trees, we prove that the statistic 'number of exterior pairs', introduced by A. Denise and R. Simion, on the set C_{n} is equidistributed with the statistic 'number of up steps at height h with h ≡ 0 (mod 3)'. Moreover, for m ≥ 3, we prove that the two statistics 'number of up steps at height h with h ≡ 0 (mod m)' and 'number of up steps at height h with h ≡ m - 1 (mod m)' on the set C_{n} are 'almost equidistributed'. Both results are proved combinatorially.

原文 | 英語 |
---|---|

期刊 | Electronic Journal of Combinatorics |

卷 | 18 |

發行號 | 1 |

出版狀態 | 已發佈 - 2011 五月 12 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics

## 指紋 深入研究「Exterior pairs and up step statistics on Dyck paths」主題。共同形成了獨特的指紋。

## 引用此

Eu, S-P., & Fu, T. S. (2011). Exterior pairs and up step statistics on Dyck paths.

*Electronic Journal of Combinatorics*,*18*(1).