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A note on large Kakeya sets

Tijdschriftbijdrage - Tijdschriftartikel

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 Z. We improve on this result by showing that Kakeya set of size at least approximate to q(2) - q root q + 3/2-q contain a large knot, and we obtain a sharp result for planes containing a Baer subplane.
Tijdschrift: ADVANCES IN GEOMETRY
ISSN: 1615-7168
Issue: 3
Volume: 21
Pagina's: 401 - 405
Jaar van publicatie:2021
Toegankelijkheid:Open