LCP
Set additivity and growth
We develop the theory of the additive dimension , i.e. the size of a maximal dissociated subset of a set . It was shown that the additive dimension is closely connected with the growth of higher sumsets of our set . We apply this approach to demonstrate that for any small multiplicative subgroup the sequence grows very fast. Also, we obtain a series of applications to the sum--product phenomenon and to the Balog--Wooley decomposition--type results.
Discrete Mathematics, in press (2023)