Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 3851-3865 |
| Number of pages | 15 |
| Journal | Journal of the European Mathematical Society |
| Volume | 19 |
| Issue number | 12 |
| DOIs | |
| State | Published - 2017 |
Bibliographical note
Publisher Copyright:© European Mathematical Society 2017.
Keywords
- Componentwise linear ideals
- Face numbers
- Sequential Cohen-Macaulayness
- Simplicial complex
- Stanley-Reisner rings