On S-(p, q)-Dyck paths | |
Hu, Han ; Zhao, Feng ; Zhao, Tongyuan | |
2016 | |
关键词 | lattice paths generalized Dyck paths Motzkin numbers generating functions GENERALIZED DYCK PATHS ENUMERATION |
英文摘要 | Bizley [J. Inst. Actuar. 80 (1954), 55-62] studied a generalization of Dyck paths from (0, 0) to (pn, qn) (gcd(p, q) = 1), which never go below the line py = qx and are made of steps in {(0,1), (1,0)1, called step set, and calculated the number of such paths. In this paper, we mainly generalize Bizley's results to an arbitrary step set S. We call these paths S-(p, q)-Dyck paths, and give explicit enumeration formulas of such paths. In addition, we provide a proof of these formulas by the method raised in Gessel [J. Combin. Theory Ser. A 28 (1980), no. 3, 321-337]. As applications, we calculate some examples which generalize the classical Schroder and Motzkin numbers.; 973 Program [2013CB834201]; SCI(E); ARTICLE; vanilla@pku.edu.cn; zhf327@pku.edu.cn; zhaotongyuan@cup.edu.cn; 225-246; 125 |
语种 | 英语 |
出处 | SCI |
出版者 | ARS COMBINATORIA |
内容类型 | 其他 |
源URL | [http://hdl.handle.net/20.500.11897/457545] ![]() |
专题 | 数学科学学院 |
推荐引用方式 GB/T 7714 | Hu, Han,Zhao, Feng,Zhao, Tongyuan. On S-(p, q)-Dyck paths. 2016-01-01. |
个性服务 |
查看访问统计 |
相关权益政策 |
暂无数据 |
收藏/分享 |
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。
修改评论