Geodesic
Face numbers of sequentially Cohen–Macaulay complexes and Betti numbers of componentwise linear ideals
Journal of the European Mathematical Society, Tome 19 (2017) no. 12, pp. 3851-3865.

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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
DOI : 10.4171/jems/755
Classification : 05-XX, 13-XX
Keywords: Simplicial complex, face numbers, Stanley–Reisner rings, sequential Cohen–Macaulayness, componentwise linear ideals 
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     author = {Karim A. Adiprasito and Anders Bj\"orner and Afshin Goodarzi},
     title = {Face numbers of sequentially {Cohen{\textendash}Macaulay} complexes and {Betti} numbers of componentwise linear ideals},
     journal = {Journal of the European Mathematical Society},
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     doi = {10.4171/jems/755},
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Karim A. Adiprasito; Anders Björner; Afshin Goodarzi. Face numbers of sequentially Cohen–Macaulay complexes and Betti numbers of componentwise linear ideals. Journal of the European Mathematical Society, Tome 19 (2017) no. 12, pp. 3851-3865. doi : 10.4171/jems/755. http://geodesic.mathdoc.fr/articles/10.4171/jems/755/

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