On the size of finite Sidon sets
UDC 519.1 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 $\mathca...
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| Дата: | 2024 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7858 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 519.1
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 $n^{1/2}+0.99703 n^{1/4}.$ |
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| DOI: | 10.3842/umzh.v76i8.7858 |