On k-simplexes in (2k-1)-dimensional vector spaces over finite fields

2009/03/13 by Lê 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

paper · pdf · doi:10.48550/arxiv.0903.2506

openalex publication_date 2009/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if the cardinality of a subset of the (2k-1)-dimensional vector space over a finite field with q elements is ≫ q^{2k-1-(1)/(2k)}, then it contains a positive proportional of all k-simplexes up to congruence.

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