On the size of finite Sidon sets
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916474455588864 |
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| author | O'Bryant, Kevin |
| author_facet | O'Bryant, Kevin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_07800 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the size of finite Sidon sets O'Bryant, Kevin Number Theory Combinatorics 11B50 (Primary) 11B83, 05B10 (Secondary) 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. |
| title | On the size of finite Sidon sets |
| topic | Number Theory Combinatorics 11B50 (Primary) 11B83, 05B10 (Secondary) |
| url | https://arxiv.org/abs/2207.07800 |