@article{O’Bryant_2024, title={On the size of finite Sidon sets}, volume={76}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/7858}, DOI={10.3842/umzh.v76i8.7858}, abstractNote={<p>UDC 519.1</p> <p>A Sidon set (also called a Golomb ruler) is a $B_2$ sequence and a $1$-thin set is a set of integers containing no nontrivial solutions to the equation $a+b=c+d.$ We improve the lower bound for the diameter of a Sidon set with $k$ elements, namely, if $k$ is sufficiently large and $\mathcal A$ is a Sidon set with $k$ elements, then ${\rm diam}({\mathcal A})\ge k^2-1.99405 k^{3/2}.$ Alternatively, if $n$ is sufficiently large, then the cardinality of the largest subset of $\{1,2,\dots,n\},$ which is a Sidon set, does not exceed $n^{1/2}+0.99703 n^{1/4}.$</p>}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={O’BryantKevin}, year={2024}, month={Sep.}, pages={1192 - 1206} }