Ruzsa's problem on Bi-Sidon sets
| Autor: | Pach, János, Zakharov, Dmitrii |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $f(N)\geq cN^{1/3}$, for a constant $c>0$. In this note, we improve this bound to $cN^{5/12}$. Comment: 7 pages |
| Databáze: | arXiv |
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