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Simplices in thin subsets of Euclidean spaces

Alex Iosevich and Ákos Magyar

Vol. 16 (2023), No. 7, 1485–1496
Abstract

Let Δ be a nondegenerate simplex on k vertices. We prove that there exists a threshold sk < k such that any set A k of Hausdorff dimension dimA sk necessarily contains a similar copy of the simplex Δ.

Keywords
simplexes, Hausdorff dimension, graphs
Mathematical Subject Classification
Primary: 28A75, 42B15
Milestones
Received: 7 September 2020
Revised: 28 September 2021
Accepted: 19 November 2021
Published: 21 September 2023
Authors
Alex Iosevich
Department of Mathematics
University of Rochester
Rochester, NY
United States
Ákos Magyar
Department of Mathematics
The University of Georgia
Athens, GA
United States

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