Ruzsa's problem on Bi-Sidon sets
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910602456203264 |
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| author | Pach, János Zakharov, Dmitrii |
| author_facet | Pach, János Zakharov, Dmitrii |
| contents | A subset $S$ of real numbers is called bi-Sidon if it is a Sidon set with respect to both addition and multiplication, i.e., if all pairwise sums and all pairwise products of elements of $S$ are distinct. Imre Ruzsa asked the following question: What is the maximum number $f(N)$ such that every set $S$ of $N$ real numbers contains a bi-Sidon subset of size at least $f(N)$? He proved that $f(N)\geq cN^{\frac13}$, for a constant $c>0$. In this note, we improve this bound to $N^{\frac13+\frac7{78}+o(1)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03128 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ruzsa's problem on Bi-Sidon sets Pach, János Zakharov, Dmitrii Combinatorics A subset $S$ of real numbers is called bi-Sidon if it is a Sidon set with respect to both addition and multiplication, i.e., if all pairwise sums and all pairwise products of elements of $S$ are distinct. Imre Ruzsa asked the following question: What is the maximum number $f(N)$ such that every set $S$ of $N$ real numbers contains a bi-Sidon subset of size at least $f(N)$? He proved that $f(N)\geq cN^{\frac13}$, for a constant $c>0$. In this note, we improve this bound to $N^{\frac13+\frac7{78}+o(1)}$. |
| title | Ruzsa's problem on Bi-Sidon sets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.03128 |