Two Bijections on Weighted Motzkin Paths  

作　　者：Chen Zhong-jin Zhao Shuo 

机构地区：[1]School of Mathematics,Beijing Technology and Business University,Beijing,100048

出　　处：《Communications in Mathematical Research》2017年第2期149-159,共11页数学研究通讯（英文版）

基　　金：The NSF(11601020,11501014)of China;Organization Department of Beijing Municipal Committee(2013D005003000012);Science and Technology Innovation Platform-Business Project 2017(PXM2017_014213_000022)

摘　　要：In this paper, we provide a bijection between the set of underdiagonal lattice paths of length n and the set of(2, 2)-Motzkin paths of length n. Besides, we generalize the bijection of Shapiro and Wang(Shapiro L W, Wang C J. A bijection between 3-Motzkin paths and Schr¨oder paths with no peak at odd height. J. Integer Seq., 2009, 12: Article 09.3.2.) to a bijection between k-Motzkin paths and(k-2)-Schr¨oder paths with no horizontal step at even height. It is interesting that the second bijection is a generalization of the well-known bijection between Dyck paths and 2-Motzkin paths.In this paper, we provide a bijection between the set of underdiagonal lattice paths of length n and the set of(2, 2)-Motzkin paths of length n. Besides, we generalize the bijection of Shapiro and Wang(Shapiro L W, Wang C J. A bijection between 3-Motzkin paths and Schr¨oder paths with no peak at odd height. J. Integer Seq., 2009, 12: Article 09.3.2.) to a bijection between k-Motzkin paths and(k-2)-Schr¨oder paths with no horizontal step at even height. It is interesting that the second bijection is a generalization of the well-known bijection between Dyck paths and 2-Motzkin paths.

关 键 词：underdiagonal lattice path (2 2)-Motzkin path k-Motzkin path (k-2)-Schrder path 

分 类 号：O157.5[理学—数学]