期刊論文
| 學年 | 113 |
|---|---|
| 學期 | 2 |
| 出版（發表）日期 | 2025-07-30 |
| 作品名稱 | Meanders and Dyck-path billiards |
| 作品名稱（其他語言） | |
| 著者 | Sen-Peng Eu; Tung-Shan Fu; Hsiang-Chun Hsu |
| 單位 | |
| 出版者 | |
| 著錄名稱、卷期、頁數 | RAIRO-Theoretical Informatics and Applications, 59(2025), 3 |
| 摘要 | We study a statistic traj on the ordered pairs (P,Q) of Dyck paths of size n, which counts the number of billiard trajectories in the grid polygon enclosed by P and Q, where Q is the path obtained by reflecting Q over the ground line. In terms of grid polygon, we establish an involution on the set of such ordered pairs (P,Q) which either increases or decreases traj(P,Q) by 1. This proves a result by Di Francesco-Golinelli-Guitter that the numbers of semimeanders (meanders, respectively) of order n with even and odd numbers of components are equal if n is even and differ by a Catalan number (the square of a Catalan number, respectively) if n is odd. Some results about ( 1)-evaluation of the generating functions for the statistic traj on restricted sets of Dyck paths are also presented. |
| 關鍵字 | Bijection; Dyck path; Meander; Trajectory |
| 語言 | en_US |
| ISSN | 0988-3754 |
| 期刊性質 | 國外 |
| 收錄於 | SCI |
| 產學合作 | |
| 通訊作者 | |
| 審稿制度 | 是 |
| 國別 | TWN |
| 公開徵稿 | |
| 出版型式 | ,電子版 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/127827 ) |