k-configurations of points in discrete self-similar sets.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I, Fractals in Pure Mathematic, Contemporary Mathematics, 600, Amer. Math. Soc., 2013, (30 pages).International audienceThis paper uses the method of zeta functions to study k-con gurations and distinct volumes of k-simplices determined by k-tuples of points of a discrete fractal set F for which the similarity transformations pairwise commute. Under certain reasonable hypotheses on F, we fi nd nontrivial lower bounds for the number of distinct k-con gurations of points and of the number of distinct volumes in increasing families of bounded subsets of F^k