Richard Oberlin
Published 2014-12-17Version 1
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.
On directions determined by subsets of vector spaces over finite fields
Ubiquity of simplices in subsets of vector spaces over finite fields
Averages and maximal averages over Product j-varieties in finite fields
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