2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72470We count a large class of lattice paths by using factorizations of free monoids. Besides the classical lattice paths counting problems related to Catalan numbers, we give a new approach to the problem of counting walks on the slit plane (walks avoid a half line) that was first solved by Bousquet-Mélou and Schaeffer. We also solve a problem about walks in the half plane avoiding a half line by subsequently applying the factorizations of two different Gessel pairs, giving a generalization of a result of Bousquet-Mélou.12 pagesCombinatoricsProbability05A15 (primary) 30B10, 82A67 (secondary)text