Ruzsa’s Problem on Bi-Sidon Sets
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493_2025_Article_151.pdf
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Author(s)
Pach, János
Zakharov, Dmitrii
Date Issued
April 8, 2025
Journal
Combinatorica
Publisher
Springer Berlin Heidelberg
Citation
Pach, J., Zakharov, D. Ruzsa’s Problem on Bi-Sidon Sets. Combinatorica 45, 26 (2025).
Version
Final published version
Abstract
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 ) ⩾ c N 1 3 , for a constant c > 0 . In this note, we improve this bound to N 1 3 + 7 78 + o ( 1 ).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00493-025-00151-5
