2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67297Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures. ``Singularity analysis'' reviewed here provides constructive estimates that are applicable in several areas of combinatorics. It constitutes a complex-analytic Tauberian procedure by which combinatorial constructions and asymptotic--probabilistic laws can be systematically related.Combinatorics05A15, 05A16, 30B10, 39B05, 60C05, 60F05, 68Q25text