Abstract
A numerical characterization is given of the h -triangles of sequentially Cohen–Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay–Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree ≤ d and shifted pure (d–1) -dimensional simplicial complexes
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