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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 l2-Euler characteristic of right-angled buildings. When L is a triangulation of a sphere we obtain a new formula for the l2-Euler characteristic

<I>f</I>-polynomials, <I>h</I>-polynomials and <I>l</I><SUP>2</SUP>-Euler characteristics