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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00947525
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Submitted on : Sunday, February 16, 2014 - 8:19:17 PM
Last modification on : Friday, March 8, 2019 - 9:38:03 AM

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  • HAL Id : hal-00947525, version 1

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

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