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math.AC2015
Dimension filtration, sequential Cohen--Macaulayness and a new polynomial invariant of graded algebras
Afshin Goodarzi
Let $\k$ be a field and let be a standard -graded $\k$-algebra. Using numerical information of some invariants in the primary decomposition of in , namely th…
math.CO2015
Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals
Karim A. Adiprasito, Anders Björner, Afshin Goodarzi
A numerical characterization is given of the so-called h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result characterizes the number of faces of various dim…