An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density in finite field geometries

2008/04/30 by David Covert, Derrick Hart, Covert, David +5 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CA #math.CO

paper · pdf · doi:10.48550/arxiv.0804.4894

arxiv created 2008/04/30 · openalex publication_date 2008/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if the cardinality of a subset of the 2-dimensional vector space over a finite field with q elements is ≥ ρq², with (1)/(√(q))<<ρ≤ 1, then it contains an isometric copy of ≥ cρq³ triangles.

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