A note on large Kakeya sets
Abstract
A Kakeya set c in an affine plane of order q is the point set covered by a set L of q + 1 pairwise non-parallel lines. By Dover and Mellinger [6], Kakeya sets with size at least q2 - 3q + 9 contain a large knot, i.e. a point of K lying on many lines of L. We improve on this result by showing that Kakeya set of size at least ≈ q2 - qq$\begin{array}{} \displaystyle \sqrt{q} \end{array}$ +32$\begin{array}{} \displaystyle \frac{3}{2} \end{array}$q contain a large knot, and we obtain a sharp result for planes containing a Baer subplane.
Publication Title
Advances in Geometry
Recommended Citation
De Boeck, M., & Van De Voorde, G. (2021). A note on large Kakeya sets. Advances in Geometry, 21 (3), 401-405. https://doi.org/10.1515/advgeom-2021-0018
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