# UNIONS OF LINES IN

@article{Oberlin2014UNIONSOL, title={UNIONS OF LINES IN}, author={Richard Oberlin}, journal={Mathematika}, year={2014}, volume={62}, pages={738-752} }

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.

## 2 Citations

### Unions of lines in $\mathbb{R}^n$

- Mathematics
- 2022

We prove a conjecture of D. Oberlin on the dimension of unions of lines in R n . If d ≥ 1 is an integer, 0 ≤ β ≤ 1, and L is a set of lines in R n with Hausdorﬀ dimension at least 2( d − 1) + β ,…

### On the Sizes of Unions of Circles over Finite Fields

- Mathematics
- 2020

This paper considers unions of circles over finite fields. We generalize an approach used by Oberlin, where in place of unions of lines we consider unions of circles. First we prove that there exists…

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