Congruence classes of triangles in \mathbbF_p²

2016/10/24 by Pham Van Thang, Van Thang, Pham, Lê Anh Vinh +1
Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1610.07408

openalex publication_date 2016/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we give a lower bound on the number of congruence classes of triangles in a small set of points in \mathbbF_p². More precisely, for A⊂ \mathbbF_p² with |A|≤ p^2/3, we prove that the number of congruence classes of triangles determined by points in A× A is at least |A|^7/2. This note is not intended for journal publication.

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