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Article Dans Une Revue Combinatorica Année : 2016

Maximal sets with no solution to x + y = 3z

Résumé

In this paper, we are interested in a generalization of the notion of sum-free sets. We address a conjecture first made in the 90s by Chung and Goldwasser. Recently, after some computer checks, this conjecture was formulated again by Matolcsi and Ruzsa, who made a first significant step towards it. Here, we prove the full conjecture by giving an optimal upper bound for the Lebesgue measure of a 3-sum-free subset A of [0, 1], that is, a set containing no solution to the equation x + y = 3z where x, y and z are restricted to belong to A. We then address the inverse problem and characterize precisely, among all sets with that property, those attaining the maximal possible measure.
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Dates et versions

hal-01096368 , version 1 (23-02-2016)

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Alain Plagne, Anne de Roton. Maximal sets with no solution to x + y = 3z. Combinatorica, 2016, 36 (2), pp.229-248. ⟨10.1007/s00493-015-3100-4⟩. ⟨hal-01096368⟩
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