The $\mathbf{uvu}$-avoiding $(a,b,c)$-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 $n$ is a lattice path from $(0,0)$ to $(n,0)$ in the first quadrant of the XOY-plane that consists of up st…