4 papers · 1 filter
The -avoiding -Generalized Motzkin paths with vertical steps: bijections and statistic enumerations
Yidong Sun, Weichen Wang, Cheng Sun
A generalized Motzkin path, called G-Motzkin path for short, of length is a lattice path from to in the first quadrant of the XOY-plane that consists of up st…
Some statistics on generalized Motzkin paths with vertical steps
Yidong Sun, Di Zhao, Wenle Shi +1
Recently, several authors have considered lattice paths with various steps, including vertical steps permitted. In this paper, we consider a kind of generalized Motzkin paths, call…
Weighted Dyck paths with special restrictions on the levels of valleys
Yidong Sun, Qianqian Liu, Yanxin Liu
This paper concentrates on the set of weighted Dyck paths of length with special restrictions on the level of valleys. We first give its explicit formula of th…
Symmetric and asymmetric peaks or valleys in (partial) Dyck paths
Yidong Sun, Wenle Shi, Di Zhao
The concepts of symmetric and asymmetric peaks in Dyck paths were introduced by Flórez and Ram\'ırez, who counted the total number of such peaks over all Dyck paths of a given leng…