Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals
Combinatorics
2017-03-06 v2 Commutative Algebra
Abstract
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 dimensions and codimensions 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 at most d and shifted pure (d-1)-dimensional simplicial complexes.
Keywords
Cite
@article{arxiv.1502.01183,
title = {Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals},
author = {Karim A. Adiprasito and Anders Björner and Afshin Goodarzi},
journal= {arXiv preprint arXiv:1502.01183},
year = {2017}
}
Comments
11 pages, 1 figure