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SIDON SETS IN A UNION OF INTERVALS

Abstract

We study the maximum size of Sidon sets in unions of integer intervals. If \(A\subset\mathbb{N}\) is the union of two intervals and if \( |A| =n\) (where \( |A| \) denotes the cardinality of \(A\)), we prove that \(A\) contains a Sidon set of size at least \(0,876\sqrt{n}\). On the other hand, by using the small differences technique, we establish a bound of the maximum size of Sidon sets in the union of \(k\) intervals.

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Acknowledgements

I would like to thank A. Plagne for having introduced me to the study of Sidon sets. Also, I would like to thank A. de Roton for her help and her many advices. Finally I am grateful to the referee for careful reading and comments.

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Correspondence to R. RIBLET.

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RIBLET, R. SIDON SETS IN A UNION OF INTERVALS. Acta Math. Hungar. 167, 533–547 (2022). https://doi.org/10.1007/s10474-022-01246-x

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  • DOI: https://doi.org/10.1007/s10474-022-01246-x

Key words and phrases

  • Sidon set
  • sequence
  • interval
  • arithmetic combinatorics

Mathematics Subject Classification

  • 11B30
  • 43A46