论文标题
大凯基（Kakeya）套装的注释
A note on large Kakeya sets
论文作者
论文摘要
Kakeya集合$ \ Mathcal {K} $在订单$ Q $的仿射平面上是$ \ Mathcal {l} $ $ q+1 $ $ 1 $ pairwise non-Parallalel Line的设置。 Dover和Mellinger研究了大型Kakeya套装。在[6]中，他们表明Kakeya设置的大小至少$ q^2-3q+9 $包含一个大结（$ \ Mathcal {k} $的点，位于$ \ Mathcal {l} $的许多行上）。在本文中，我们通过显示至少$ \ of $ \ of $ \ of q^2-q \ sqrt {q}+\ frac {3} {2} q $包含一个大结的Kakeya集。此外，我们获得了包含Baer子平面的平方顺序平面的鲜明结果。
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.
