Functiones et Approximatio Commentarii Mathematici

On Sidon sets which are asymptotic bases of order $4$

Sándor Z. Kiss, Eszter Rozgonyi, and Csaba Sándor

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Let $h \geq 2$ be an integer. We say that a set $\mathcal{A}$ of positive integers is an asymptotic basis of order $h$ if every large enough positive integer can be represented as the sum of $h$ terms from $\mathcal{A}$. A set of positive integers $\mathcal{A}$ is called a Sidon set if all the sums $a+b$ with $a,b \in \mathcal{A}$, $a \leq b$ are distinct. In this paper we prove the existence of Sidon set $\mathcal{A}$ which is an asymptotic basis of order $4$ by using probabilistic methods.

Article information

Funct. Approx. Comment. Math., Volume 51, Number 2 (2014), 393-413.

First available in Project Euclid: 26 November 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11B13: Additive bases, including sumsets [See also 05B10]
Secondary: 11B75: Other combinatorial number theory

additive number theory representation functions Sidon set asymptotic basis


Kiss, Sándor Z.; Rozgonyi, Eszter; Sándor, Csaba. On Sidon sets which are asymptotic bases of order $4$. Funct. Approx. Comment. Math. 51 (2014), no. 2, 393--413. doi:10.7169/facm/2014.51.2.10.

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  • J. Cilleruelo, Sidon basis, arXiv: 1304.5351.
  • J.M. Deshouillers, A. Plagne, A Sidon basis, Acta Mathematica Hungarica 123 (2009), 233–238.
  • G. Grekos, L. Haddad, C. Helou, J. Pihko, Representation functions, Sidon sets and bases, Acta Arithmetica 130(2) (2007), 149–156.
  • H. Halberstam, K.F. Roth, Sequences, Springer–Verlag, New York, 1983.
  • J.H. Kim and V.H. Vu, Concentration of multivariate polynomials and its applications, Combinatorica 20 (2000), 417–434.
  • S.Z. Kiss, On Sidon sets which are asymptotic bases, Acta Mathematica Hungarica 128 (2010), 46–58.
  • M.B. Nathanson, Additive Number Theory The Classical Bases, Springer, 1996
  • T. Tao, V.H. Vu, Additive Combinatorics, Cambridge University Press, 2006.
  • V.H. Vu, On the concentration of multi-variate polynomials with small expectation, Random Structures and Algorithms 16 (2000), 344–363.
  • V.H. Vu, Chernoff type bounds for sum of dependent random variables and applications in additive number theory, Number theory for the millennium, III (Urbana, IL, 2000), 341–356, A K Peters, Natick, MA, 2002.