雷代方向数定理的新证明

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-04-08 DOI:10.1007/s00013-024-01979-x

Gábor Somlai

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引用次数: 0

摘要

Rédei 和 Megyesi 证明了由\({\mathbb F}_p^2\) 的 p 元素子集决定的方向数要么是 1 要么至少是 \(\frac{p+3}{2}\)。德雷斯、克林和穆兹丘克也独立地得到了同样的结果。我们利用基斯和作者证明的一个lemma，对这一结果给出了一个新的简短证明。新的证明依赖于有限域上多项式的一个结果。

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A new proof of Rédei’s theorem on the number of directions

Rédei and Megyesi proved that the number of directions determined by a p-element subset of \({\mathbb F}_p^2\) is either 1 or at least \(\frac{p+3}{2}\). The same result was independently obtained by Dress, Klin, and Muzychuk. We give a new and short proof of this result using a lemma proved by Kiss and the author. The new proof relies on a result on polynomials over finite fields.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.