On a Furstenberg-Katznelson-Weiss type theorem over finite fields

2008/07/17 by Lê Anh Vinh, Le Anh Vinh, Vinh, Le Anh
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #math.CO

paper · pdf · doi:10.48550/arxiv.0807.2849

arxiv created 2008/07/17 · openalex publication_date 2008/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 >= rq², with q^-1/2 << r <= 1 then it contains an isometric copy of >= crq³ triangles. In this note, we give a graph theoretic proof of this result.

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