TY - JOUR
AU - Kevin O'Bryant
PY - 2024/09/04
Y2 - 2024/10/12
TI - On the size of finite Sidon sets
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 76
IS - 8
SE - Research articles
DO - 10.3842/umzh.v76i8.7858
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/7858
AB - UDC 519.1A 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 $n^{1/2}+0.99703 n^{1/4}.$
ER -