2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78923We define an n-dimensional polytope Pi_n(x), depending on parameters x_i>0, whose combinatorial properties are closely connected with empirical distributions, plane trees, plane partitions, parking functions, and the associahedron. In particular, we give explicit formulas for the volume of Pi_n(x) and, when the x_i's are integers, the number of integer points in Pi_n(x). We give two polyhedral decompositions of Pi_n(x), one related to order cones of posets and the other to the associahedron.41 pagesCombinatorics52B12; 05A15text