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

Authors
  • Hart, Derrick
  • Iosevich, Alex
  • Koh, Doowon
  • Senger, Steve
  • Uriarte-Tuero, Ignacio
Type
Preprint
Publication Date
Apr 18, 2008
Submission Date
Apr 18, 2008
Source
arXiv
License
Yellow
External links

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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