Abstract
A Kakeya set π in an affine plane of order q is the point set covered by a set π of q + 1 pairwise non-parallel lines. By Dover and Mellinger [6], Kakeya sets with size at least q2 β 3q + 9 contain a large knot, i.e. a point of π lying on many lines of π. We improve on this result by showing that Kakeya set of size at least β q2 β q
Communicated by: J. Bamberg
Acknowledgements
This research was partially carried out when the first author was visiting the School of Mathematics and Statistics at the University of Canterbury. He wants to thank the School, and in particular the second author, for their hospitality.
We thank the anonymous reviewers for their detailed suggestions.
References
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