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Distance sets of two subsets of vector spaces over finite fields


Authors: Doowon Koh and Hae-Sang Sun
Journal: Proc. Amer. Math. Soc. 143 (2015), 1679-1692
MSC (2010): Primary 52C10, 11T23
DOI: https://doi.org/10.1090/S0002-9939-2014-12386-0
Published electronically: December 15, 2014
MathSciNet review: 3314081
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Abstract: We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we improve upon the results by Rainer Dietmann. In the case that one of the subsets is a product set, we obtain further improvement on the estimate.


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Additional Information

Doowon Koh
Affiliation: Department of Mathematics, Chungbuk National University, Cheongju, Chungbuk 361-763, Republic of Korea
Email: koh131@chungbuk.ac.kr

Hae-Sang Sun
Affiliation: Department of Mathematics, Chungbuk National University, Cheongju, Chungbuk 361-763, Republic of Korea
Address at time of publication: Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, UNIST-gil 50, Ulsan 689-798, Republic of Korea
Email: haesang@chungbuk.ac.kr, haesang.sun@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-12386-0
Keywords: Erd\H{o}s distance problem, finite fields
Received by editor(s): April 20, 2013
Published electronically: December 15, 2014
Additional Notes: The first and second authors were supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1001510, 2010-0023248)
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society