f-vectors of acyclic complexes
For a finite simplicial complex C and for \(k\geq -1\) denote \(f_ k(C)=\{S\in C:\) \(| S| =k+1\}\). The vector \(f(C)=(f_ 0(C),f_ 1(C),...)\) is the f-vector of C. The purpose of this note is to present a characterization of f-vectors of (finite) acyclic simplicial complexes. The characterization is by one well-known relation \(\chi (C)=1\) and a system of inequalities.
scientific article; zbMATH DE number 3927924