  We 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.
