Unions of lines in F^n

Abstract

We show that if a collection of lines in a vector space over a finite field has "dimension" at least 2(d-1) + beta, then its union has "dimension" at least d + beta. This is the sharp estimate of its type when no structural assumptions are placed on the collection of lines. We also consider some refinements and extensions of the main result, including estimates for unions of k-planes.

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References in corpus (2)

• On the size of Kakeya sets in finite fields
• The Kakeya set and maximal conjectures for algebraic varieties over finite fields

Cited by in corpus (1)

• Unions of lines in ${\mathbb{R}}^n$