Set additivity and growth
Combinatorics
The additive dimension of a set, which is the size of a maximal dissociated subset, is closely connected to the rapid growth of higher sumsets.
Additive dimension and the growth of sets
Discrete Mathematics, in press
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