2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138422This thesis focuses on algebraic shifting and its applications to f-vector theory of simplicial complexes and more general graded posets. In particular, several approaches and partial results concerning the g-conjecture for simplicial spheres are presented here.PhD thesis. The results in Chapter 4 will be included in a future paper. Most (but not all) of the results obtained in the other chapters had been included in papers by the author. 101 pages, 2 figuresCombinatoricstext