A note on large Kakeya sets-Reference-Cited by-同舟云学术

A note on large Kakeya sets

Published:2021-07-01 Issue:3 Volume:21 Page:401-405
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

De Boeck Maarten¹²,Van de Voorde Geertrui³

Affiliation:

1. Eindhoven University of Technology , Department of Mathematics and Computer Science , Groene loper 5, 5612 AZ , Eindhoven , The Netherlands

2. Ghent University , Department of Mathematics: Algebra and Geometry , Krijgslaan 281–S25, 9000 Gent , Flanders , Belgium

3. University of Canterbury , School of Mathematics and Statistics , Private Bag 4800, 8140 , Christchurch , New Zealand

Abstract

Abstract A Kakeya set 𝓚 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 q 2 – 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 ≈ q 2 – q + q contain a large knot, and we obtain a sharp result for planes containing a Baer subplane.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2021-0018/pdf

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