Primitive Dyck words as an invariance class for pattern avoidance

In this paper we study the construction and the enumeration of particular binary words avoiding a primitive Dyck word. We give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words and then kills those containing the forbidden pattern. Then, we give the generating function of such words according to the number of ones. Finally, a more general algorithm that generates binary words avoiding a set of primitive Dyck words is given.