Betti numbers of Stanley--Reisner rings with pure resolutions

Gabor Hegedüs

Betti numbers of Stanley--Reisner rings with pure resolutions

Commutative Algebra 2011-02-01 v2 Combinatorics

Authors: Gabor Hegedüs

Abstract

Let $\Delta$ be simplicial complex and let $k[\Delta]$ denote the Stanley--Reisner ring corresponding to $\Delta$ . Suppose that $k[\Delta]$ has a pure free resolution. Then we describe the Betti numbers and the Hilbert--Samuel multiplicity of $k[\Delta]$ in terms of the $h$ --vector of $\Delta$ . As an application, we derive a linear equation system for the components of the $h$ --vector of the clique complex of an arbitrary chordal graph.

Keywords

Stanley-Reisner ring pure free resolution Betti numbers Hilbert-Samuel multiplicity h-vector simplicial complex chordal graph

Cite

@article{arxiv.1101.5565,
  title  = {Betti numbers of Stanley--Reisner rings with pure resolutions},
  author = {Gabor Hegedüs},
  journal= {arXiv preprint arXiv:1101.5565},
  year   = {2011}
}

Comments

10 pages, new formulas for the components of the clique complex of chordal graphs

Betti numbers of Stanley--Reisner rings with pure resolutions

Abstract

Keywords

Cite

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