On kaleidoscopic pseudo-randomness of finite Euclidean graphs

TL;DR

This paper investigates the pseudo-random properties of finite Euclidean graphs, demonstrating that large subsets of vector spaces over finite fields contain all finite configurations, using probabilistic techniques.

Contribution

It introduces new probabilistic methods to analyze the kaleidoscopic pseudo-randomness of finite Euclidean graphs and shows their rich combinatorial structure.

Findings

Large subsets contain all finite configurations

Finite Euclidean graphs exhibit kaleidoscopic pseudo-randomness

Probabilistic methods effectively analyze these properties

Abstract

In this paper we study the kaleidoscopic pseudo-randomness of finite Euclidean graphs using probabilistic methods. Roughly speaking, we show that sufficiently large subsets of d-dimensional vector spaces over finite fields contain every possible finite configurations.