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On the dimension of additive sets (1407.4987v2)
Published 18 Jul 2014 in math.CO
Abstract: 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 ${0,1}n\subset \mathbb{Z}n$.
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