2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217688Theory of Kingman's partition structures has two culminating points: the general paintbox representation, relating finite partitions to hypothetical infinite populations via a natural sampling procedure, known as Kingman's paintbox; a central example of the theory - the Ewens-Pitman two-parameter family of partitions. In these notes we further develop the theory by passing to structures enriched by the order on the collection of categories; extending the class of tractable models by exploring the idea of regeneration; analysing regenerative properties of the Ewens-Pitman partitions; studying asymptotic features of the regenerative compositions.A mini-course read at the School on Information and Randomness 2008, in Santiago de ChileProbability60G09, 60C05text