Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals

Karim A. Adiprasito*, Anders Björner, Afshin Goodarzi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageAmerican English
Pages (from-to)3851-3865
Number of pages15
JournalJournal of the European Mathematical Society
Volume19
Issue number12
DOIs
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© European Mathematical Society 2017.

Keywords

  • Componentwise linear ideals
  • Face numbers
  • Sequential Cohen-Macaulayness
  • Simplicial complex
  • Stanley-Reisner rings

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