Appears in collection : Enumerative combinatorics and effective aspects of differential equations Thematic Month Week 5 / Combinatoire énumérative et aspects effectifs des équations différentielles Mois thématique semaine 5

Lattice paths are fundamental combinatorial objects, and their enumeration has strong connections to other fields (physics, computer science). In this talk, we will review enumeration of models of lattice paths with forbidden patterns and with dynamic boundary in both one- and two-dimensional models. We will also examine how automata-based approaches often result in the simplification and classification of enumeration problems.