On Delannoy paths without peaks and valleys

Seunghyun Seo, Heesung Shin

A lattice path is called \emph{Delannoy} if its every step belongs to $\left\{N,E,D\right\}$, where $N=(0,1)$, $E=(1,0)$, and $D=(1,1)$ steps. \emph{Peak}, \emph{valley}, and \em…