Note: [] Address for correspondence: Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Viale G.B. Morgagni 65, 50134 Firenze, Italy
Abstract: In this paper we study the enumeration and the construction of particular binary words avoiding the pattern 1j+10j. By means of the theory of Riordan arrays, we solve the enumeration problem and 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.
Keywords: Binary words, pattern avoidance, succession rule, generating tree
