2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73184We consider redundant analogues of the f- and h-vectors of simplicial complexes and present bases of R^{m+1} related to these ``long'' f- and h-vectors describing the face systems from 2^{1,...,m}; we list the corresponding change of basis matrices. The representations of the long f- and h-vectors of a face system with respect to various bases are expressed based on partitions of the system into Boolean intervals.12 pagesCombinatorics13F55; 15A99text