Distance Graphs in Vector Spaces Over Finite Fields

  • Derrick Hart
  • Alex Iosevich
  • Doowon Koh
  • Steven Senger
  • Ignacio Uriarte-Tuero
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 25)

Abstract

In this chapter we systematically study various properties of the distance graph in \({\mathbb{F}}_{q}^{d}\), the d-dimensional vector space over the finite field \({\mathbb{F}}_{q}\) 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 configuration.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Derrick Hart
    • 1
  • Alex Iosevich
    • 2
  • Doowon Koh
    • 3
  • Steven Senger
    • 4
  • Ignacio Uriarte-Tuero
    • 5
  1. 1.Rutgers UniversityPiscatawayUSA
  2. 2.University of RochesterRochesterUSA
  3. 3.Chungbuk National UniversityCheongjuKorea
  4. 4.University of DelawareNewarkUSA
  5. 5.Michigan State UniversityEast LansingUSA

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