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

Published electronically:
December 15, 2014

MathSciNet review:
3314081

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Abstract | References | Similar Articles | Additional Information

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