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arXiv · 2207.07800

On the size of finite Sidon sets

Kevin O'Bryant
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Abstract

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-F\"uredi-Roy (arXiv:2103:15850v2), we use a method that is logically simpler.

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Kevin O'Bryant. 2022-07-16. On the size of finite Sidon sets. https://doi.org/10.3842/umzh.v76i8.7858

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