## On the dimension of additive sets

### Volume 167 / 2015

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

#### 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 $\{0,1\}^n\subset \mathbb Z^n$.