Geodesic
On the dimension of additive sets
P. Candela 1   ; H. A. Helfgott 2
1 Alfréd Rényi Institute of Mathematics 13-15 Reáltanoda u. 1053 Budapest, Hungary
2 IMJ-PRG, UMR 7586 Bâtiment S. Germain, case 7012 58 avenue de France 75013 Paris, France
Acta Arithmetica, Tome 167 (2015) no. 1, pp. 91-100 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\{0,1\}^n\subset \mathbb Z^n$.
DOI : 10.4064/aa167-1-5
Keywords: study relations between several notions dimension additive set which well known which recent appearing instance work schoen shkredov obtain bounds ratios between these dimensions improving inequality lev yuster these bounds asymptotically sharp using particular existence large dissociated subsets subset mathbb

P. Candela  1   ; H. A. Helfgott  2

1 Alfréd Rényi Institute of Mathematics 13-15 Reáltanoda u. 1053 Budapest, Hungary
2 IMJ-PRG, UMR 7586 Bâtiment S. Germain, case 7012 58 avenue de France 75013 Paris, France 
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P. Candela; H. A. Helfgott. On the dimension of additive sets. Acta Arithmetica, Tome 167 (2015) no. 1, pp. 91-100. doi: 10.4064/aa167-1-5

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