English

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

Combinatorics 2008-04-21 v1

Abstract

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

Keywords

Cite

@article{arxiv.0804.3036,
  title  = {Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness},
  author = {Derrick Hart and Alex Iosevich and Doowon Koh and Steve Senger and Ignacio Uriarte-Tuero},
  journal= {arXiv preprint arXiv:0804.3036},
  year   = {2008}
}
R2 v1 2026-06-21T10:32:35.184Z