Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness

2008/04/18 by Derrick Hart, Alex Iosevich, Hart, Derrick +7
Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.0804.3036

openalex publication_date 2008/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we systematically study various properties of the distance graph in \Bbb F_q^d, the d-dimensional vector space over the finite field \Bbb F_q with q elements. In the process we compute the diameter of distance graphs and show that sufficiently large subsets of d-dimensional vector spaces over finite fields contain every possible finite configurations.

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