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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Cilleruelo, Javier Ruzsa, Imre and Vinuesa, Carlos 2010. Generalized Sidon sets. Advances in Mathematics, Vol. 225, Issue. 5, p. 2786.
    Matolcsi, Máté and Vinuesa, Carlos 2010. Improved bounds on the supremum of autoconvolutions. Journal of Mathematical Analysis and Applications, Vol. 372, Issue. 2, p. 439.
    Cilleruelo, Javier 2010. Sidon sets in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi mathvariant="double-struck">N</mml:mi><mml:mi>d</mml:mi></mml:msup></mml:math>. Journal of Combinatorial Theory, Series A, Vol. 117, Issue. 7, p. 857.
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B2[g] Sets and a Conjecture of Schinzel and Schmidt

  • JAVIER CILLERUELO (a1) and CARLOS VINUESA (a1)
Abstract

A set of integers is called a B2[g] set if every integer m has at most g representations of the form m = a + a′, with a ≤ a′ and a, a′ ∈ . We obtain a new lower bound for F(g, n), the largest cardinality of a B2[g] set in {1,. . .,n}. More precisely, we prove that infn→∞ where ϵg → 0 when g → ∞. We show a connection between this problem and another one discussed by Schinzel and Schmidt, which can be considered its continuous version.

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COPYRIGHT: © Cambridge University Press 2008
References
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[1]Cilleruelo, J., Ruzsa, I. and Trujillo, C. (2002) Upper and lower bounds for finite B 2[g] sequences. J. Number Theory 97 26–34.
[2]Green, B. (2001) The number of squares and B h[g] sequences. Acta Arithmetica 100 365–390.
[3]Kolountzakis, M. (1996) The density of B h[g] sequences and the minimum of dense cosine sums. J. Number Theory 56 4–11.
[4]Martin, G. and O'Bryant, K. (2006) Constructions of generalized Sidon sets. J. Combin. Theory Ser. A 113 591–607.
[5]Martin, G. and O'Bryant, K. (2007) The symmetric subset problem in continuous Ramsey theory. Experiment. Math. 16 145–166.
[6]Ruzsa, I. (1993) Solving a linear equation in a set of integers I. Acta Arithmetica 65 259–282.
[7]Schinzel, A. and Schmidt, W. M. (2002) Comparison of L 1- and L ∞-norms of squares of polynomials. Acta Arithmetica 104 283–296.
[8]Tao, T. and Vu, V. (2006) Additive Combinatorics, Vol. 105 of Cambridge Studies in Advanced Mathematics, Cambridge University Press.
[9]Yu, G. (2007) An upper bound for B 2[g] sets. J. Number Theory 122 211–220.
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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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