Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"
Image for the paper "Additive dimension and the growth of sets"

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  (2023)

I. Shkredov

We develop the theory of the additive dimension dim(A)\dim(A), i.e. the size of a maximal dissociated subset of a set AA. It was shown that the additive dimension is closely connected with the growth of higher sumsets nAnA of our set AA. We apply this approach to demonstrate that for any small multiplicative subgroup Γ\Gamma the sequence nΓ|n\Gamma| 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)

I. Shkredov