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

Driss Essouabri (1, 2) , Ben Lichtin (3)

1 ICJ - Institut Camille Jordan
2 CTN - Combinatoire, théorie des nombres
3 ROCHESTER, NY, USA - Rochester, NY, USA

This 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.

Mots clés: k-con guration of points; Self-similar discrete sets; fractals; zeta functions; meromorphic continuation; Hausdorff dimension; Erdos distance problem; k-con guration of points.

Domaines: Théorie des nombres [math.NT]

Driss Essouabri, Ben Lichtin. k-configurations of points in discrete self-similar sets.. Contemporary mathematics, 2014, 600, p. 21-50. ⟨hal-00947525⟩