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Distance Graphs in Vector Spaces Over Finite Fields

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Recent Advances in Harmonic Analysis and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((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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Author information

Authors and Affiliations

  1. Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ, 08854-8019, USA

    Derrick Hart

  2. University of Rochester, 915 Hylan Building RC, Rochester, NY, 14627, USA

    Alex Iosevich

  3. Chungbuk National University, 410 Sungbong-Ro, Heungdeok-Gu, Cheongju, Chungbuk, 361-763, Korea

    Doowon Koh

  4. University of Delaware, 501 Ewing Hall, Newark, DE, 19716, USA

    Steven Senger

  5. Michigan State University, East Lansing, MI, 48824, USA

    Ignacio Uriarte-Tuero

Authors
  1. Derrick Hart
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  2. Alex Iosevich
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  3. Doowon Koh
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  4. Steven Senger
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  5. Ignacio Uriarte-Tuero
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Corresponding author

Correspondence to Alex Iosevich .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of South Carolina, Greene Street 1523, Columbia, 29208, South Carolina, USA

    Dmitriy Bilyk

  2. University Park, Department of Mathematics, Florida International University, SW 8th St., Rm 416 11200, Miami, 33199, Florida, USA

    Laura De Carli

  3. , Department of Mathematics, Universtity of Georgia, University of Georgia, Athens, 30602, Georgia, USA

    Alexander Petukhov

  4. Georgia Southern University, PO Box 8093, Statesboro, 30460, Georgia, USA

    Alexander M. Stokolos

  5. , Department of Mathematics, Georgia Institute of Technology, Cherry Street 686, Atlanta, 30332, Georgia, USA

    Brett D. Wick

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Hart, D., Iosevich, A., Koh, D., Senger, S., Uriarte-Tuero, I. (2012). Distance Graphs in Vector Spaces Over Finite Fields. In: Bilyk, D., De Carli, L., Petukhov, A., Stokolos, A., Wick, B. (eds) Recent Advances in Harmonic Analysis and Applications. Springer Proceedings in Mathematics & Statistics, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4565-4_14

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