关于大型Kakeya电视机的注意事项

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-07-01 DOI:10.1515/advgeom-2021-0018

M. de Boeck, G. Van de Voorde

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引用次数: 0

摘要

在q阶仿射平面上的Kakeya集合𝓚是由q + 1对非平行线的集合所覆盖的点集。通过Dover和Mellinger[6]，大小至少为q2 - 3q + 9的Kakeya集合包含一个大的结，即一个点𝓚位于许多条线上。我们改进了这一结果，证明大小至少≈q2 - q q $\begin{array}{} \displaystyle \sqrt{q} \end{array}$ + 32 $\begin{array}{} \displaystyle \frac{3}{2} \end{array}$ q的Kakeya集合包含一个大的结，并且对于包含Baer子平面的平面我们得到了一个清晰的结果。

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A note on large Kakeya sets

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 q2 – 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 ≈ q2 – q q $\begin{array}{} \displaystyle \sqrt{q} \end{array}$ + 32 $\begin{array}{} \displaystyle \frac{3}{2} \end{array}$q contain a large knot, and we obtain a sharp result for planes containing a Baer subplane.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.