Report
A note on large Kakeya sets
| العنوان: | A note on large Kakeya sets |
|---|---|
| المؤلفون: | De Boeck, Maarten, Van de Voorde, Geertrui |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05B25, 51E15, 51E20 |
| الوصف: | A Kakeya set $\mathcal{K}$ in an affine plane of order $q$ is the point set covered by a set $\mathcal{L}$ of $q+1$ pairwise non-parallel lines. Large Kakeya sets were studied by Dover and Mellinger; in [6] they showed that Kakeya sets with size at least $q^2-3q+9$ contain a large knot (a point of $\mathcal{K}$ lying on many lines of $\mathcal{L}$). In this paper, we improve on this result by showing that Kakeya set of size at least $\approx q^2-q\sqrt{q}+\frac{3}{2}q$ contain a large knot. Furthermore, we obtain a sharp result for planes of square order containing a Baer subplane. Comment: To appear in Advances in Geometry |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2003.08480 |
| رقم الانضمام: | edsarx.2003.08480 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |