Year: 2017
Author: Zhongjin Chen, Shuo Zhao
Communications in Mathematical Research , Vol. 33 (2017), Iss. 2 : pp. 149–159
Abstract
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 Schröder 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)-Schröder 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2017.02.07
Communications in Mathematical Research , Vol. 33 (2017), Iss. 2 : pp. 149–159
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: underdiagonal lattice path (2 2)-Motzkin path $k$-Motzkin path ($k$−2)-Schröder path