Kakeya-type sets in finite vector spaces

2010/03/19 by Swastik Kopparty, Vsevolod F. Lev, Kopparty, Swastik +5 · 1 citation
Computer Science · Mathematics · #05B25 #51E20 #52C17. #Advanced Topology and Set Theory #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1003.3736

openalex publication_date 2010/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite vector space V and a non-negative integer r≤dim V we estimate the smallest possible size of a subset of V, containing a translate of every r-dimensional subspace. In particular, we show that if K⊂ V is the smallest subset with this property, n denotes the dimension of V, and q is the size of the underlying field, then for r bounded and r

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