Ubiquity of simplices in subsets of vector spaces over finite fields

Abstract

We prove that a sufficiently large subset of the $d$-dimensional vector space over a finite field with $q$ elements, ${\mathbb{F}}_q^d$, contains a copy of every $k$-simplex. Fourier analytic methods, Kloosterman sums, and bootstrapping play an important role.

10 pages

Cited by in corpus (2)

• An elementary approach to simplexes in thin subsets of Euclidean space
• Rigidity, graphs and Hausdorff dimension