论文标题
关于有限的西顿套装的大小
On the size of finite Sidon sets
论文作者
论文摘要
Sidon集是一组整数，其中不包含公式$ a+b = c+d $的非平凡解决方案。我们改进了带有$ k $元素的Sidon套件直径的下限：如果$ k $足够大，$ {\ cal a} $是带有$ k $元素的Sidon套件，则$ k $元素，然后$ diam（{\ cal a}）\ ge k^2-1.99405 k^{3/2 {3/2/2} $。另外，如果$ n $足够大，则是$ \ {1,2，\ dots，n \} $的最大子集（Sidon set，最多具有$ n^{1/2} +0.99703 n^n^n^{1/4} $。尽管这些仅在Balogh-Füredi-Roy（Arxiv：2103：15850V2）上进行了略有数值改进，但我们使用一种在逻辑上更简单的方法。
A Sidon set is a set of integers containing no nontrivial solutions to the equation $a+b=c+d$. We improve on the lower bound on the diameter of a Sidon set with $k$ elements: if $k$ is sufficiently large and ${\cal A}$ is a Sidon set with $k$ elements, then $diam({\cal A})\ge k^2-1.99405 k^{3/2}$. Alternatively, if $n$ is sufficiently large, then the largest subset of $\{1,2,\dots,n\}$ that is a Sidon set has cardinality at most $n^{1/2}+0.99703 n^{1/4}$. While these are only slight numerical improvements on Balogh-Füredi-Roy (arXiv:2103:15850v2), we use a method that is logically simpler.
