2015/02/04 by Karim Adiprasito, Anders Björner, Adiprasito, Karim A. +3
Mathematics · #05D05 #05E40 #05E45 #13A02 #13D02 #13F55 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1502.01183
openalex publication_date 2015/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A numerical characterization is given of the so-called h-triangles of\nsequentially Cohen-Macaulay simplicial complexes. This result characterizes the\nnumber of faces of various dimensions and codimensions in such a complex,\ngeneralizing the classical Macaulay-Stanley theorem to the nonpure case.\nMoreover, we characterize the possible Betti tables of componentwise linear\nideals. A key tool in our investigation is a bijection between shifted\nmulticomplexes of degree at most d and shifted pure (d-1)-dimensional\nsimplicial complexes.\n