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 and some
inequalities for the components of the h--vector of the clique complex of an
arbitrary chordal graph. As an other application, we derive a linear equation
system and some inequalities for the components of the h--vector of
Cohen--Macaulay simplicial complexes.Comment: 18 pages, better introduction, ask for feedback before submissio