Existence of a Sidon set for the distinct distance constant

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2026-05-19 DOI:10.1007/s10474-026-01604-z

Robin Riblet, Titien Schehr

引用次数: 0

Abstract

We highlight a certain compactness of Sidon sets and \(B_2[g]\)-sets and provide several applications. Notably, we prove the existence of such sets that maximize certain functions. In particular, we show the existence of a Sidon set whose reciprocal sum is equal to the distinct distance constant. We also improve the best known bounds for this constant.

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不同距离常数的西顿集的存在性

我们强调了Sidon集和\(B_2[g]\) -集的某种紧致性，并提供了几个应用。值得注意的是，我们证明了使某些函数最大化的集合的存在性。特别地，我们证明了一个西顿集的存在性，它的倒数和等于不同距离常数。我们还改进了这个常数的已知界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.