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On the dimension of additive sets

Volume 167 / 2015

P. Candela, H. A. Helfgott Acta Arithmetica 167 (2015), 91-100 MSC: Primary 11B30; Secondary 05D40. DOI: 10.4064/aa167-1-5


We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of Schoen and Shkredov. We obtain bounds for the ratios between these dimensions by improving an inequality of Lev and Yuster, and we show that these bounds are asymptotically sharp, using in particular the existence of large dissociated subsets of $\{0,1\}^n\subset \mathbb Z^n$.


  • P. CandelaAlfréd Rényi Institute of Mathematics
    13-15 Reáltanoda u.
    1053 Budapest, Hungary
  • H. A. HelfgottIMJ-PRG, UMR 7586
    Bâtiment S. Germain, case 7012
    58 avenue de France
    75013 Paris, France

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