\(f\)-polynomials, \(h\)-polynomials, and \(l^2\)-Euler characteristics. (English) Zbl 1207.57033

Author’s abstract: We introduce a many-variable version of the \(f\)-polynomial and \(h\)-polynomial associated to a finite simplicial complex. In this context the \(h\)-polynomial is actually a rational function. We establish connections with the \(l^2\)-Euler characteristic of right-angled buildings. When \(L\) is a triangulation of a sphere we obtain a new formula for the \(l^2\)-Euler characteristic.


57Q05 General topology of complexes
57M15 Relations of low-dimensional topology with graph theory
20F55 Reflection and Coxeter groups (group-theoretic aspects)
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
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