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On a Furstenberg-Katznelson-Weiss Type Theorem over Finite Fields
Le Anh Vinh
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
vinh@math.harvard.edu
Annals of Combinatorics 15 (3) pp.541-547 July, 2011
AMS Subject Classification: 05C15, 05C80
Abstract:
Using Fourier analysis, Covert, Hart, Iosevich, and Uriarte-Tuero (2008) showed that if the cardinality of a subset of the 2-dimensional vector space over a finite field with q elements is ≥ρq2, with q−1/2≤ρ ≤ then it contains an isometric copy of ≥cρq3 triangles. In this note, we give a graph theoretic proof of this result.
Keywords: finite Euclidean graphs, pseudo-random graphs

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