An Upper Bound on the Size of Sidon Sets

A classical combinatorial number theory problem is to determine the maximum size of a Sidon set of , where a subset of integers is Sidon if all its pairwise sums are different. For this entry point into the subject, combining two elementary proofs, we decrease the gap between the upper and lower bou...

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Bibliographic Details
Published inThe American mathematical monthly Vol. 130; no. 5; pp. 437 - 445
Main Authors Balogh, József, Füredi, Zoltán, Roy, Souktik
Format Journal Article
LanguageEnglish
Published Washington Taylor & Francis 28.05.2023
Taylor & Francis Ltd
Subjects
Combinatorial analysis
Elementary school students
Estimating techniques
Lower bounds
Mathematics
MSC: 05D99
Number Concepts
Number theory
Set theory
Upper bounds
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ISSN0002-9890
1930-0972
DOI10.1080/00029890.2023.2176667

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Summary:A classical combinatorial number theory problem is to determine the maximum size of a Sidon set of , where a subset of integers is Sidon if all its pairwise sums are different. For this entry point into the subject, combining two elementary proofs, we decrease the gap between the upper and lower bounds by 0.2% for infinitely many values of n. We show that the maximum size of a Sidon set of is at most for n sufficiently large.
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ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2023.2176667