Pattern avoiding words and cross-bifix-free sets: a general approach

In this thesis we determine an algorithmic unified approach, based on the concept of succession rule, for the construction and the enumeration, according to the number of ones, of binary words in {0, 1} having the number of 1’s greater than or equal to the number of 0’s, and which can be applied to any forbidden pattern. Moreover, we extend this approach to the class of binary words in {0, 1} having the number of 1’s greater than or equal to the number of 0’s, and avoiding a set of forbidden patterns. In the second line of research, succession rules are studied posing a specific relevance on their relationships with recurrence relations.