Betti numbers of Stanley--Reisner rings with pure resolutions

2011/01/28 by Hegedüs, Gabor
#05E40 #13D02 #13D40 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.5565

Abstract

Let Δ be simplicial complex and let k[Δ] denote the Stanley--Reisner ring corresponding to Δ. Suppose that k[Δ] has a pure free resolution. Then we describe the Betti numbers and the Hilbert--Samuel multiplicity of k[Δ] in terms of the h--vector of Δ. 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.

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