2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70909We report about some results, interesting examples, problems and conjectures revolving around the parabolic Kostant partition functions, the parabolic Kostka polynomials and ``saturation'' properties of several generalizations of the Littlewood--Richardson numbers.79 pages, new sections, new results and examplesCombinatorics05E05, 05E10text