2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72983The number of flags in a complete fan, or more generally in an Eulerian poset, is encoded in the cd-index. We prove non-negativity of the cd-index for complete fans, regular CW-spheres and Gorenstein* posets.The difference between lattices and posets clarified. 19 pagesAlgebraic GeometryCombinatorics14M25; 06A07text