Partial Motzkin paths with air pockets of the first kind avoiding peaks, valleys or double rises
Partial Motzkin paths with air pockets of the first kind avoiding peaks, valleys or double rises
Motzkin paths with air pockets (MAP) of the first kind are defined as a generalization of Dyck paths with air pockets. They are lattice paths in [Formula: see text] starting at the origin made of steps [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], where …