Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals
(English)Article in journal (Other academic) Submitted
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.
IdentifiersURN: urn:nbn:se:kth:diva-186130OAI: oai:DiVA.org:kth-186130DiVA: diva2:925575
QS 20162016-05-022016-05-022016-05-16Bibliographically approved