The automorphism group of some semigroups
The cardinality of sumsets: different summands
We offer a complete answer to the following question on the growth of sumsets in commutative groups. Let h be a positive integer and be finite sets in a commutative group. We bound from above in terms of |A|, |A + B₁|, ..., and h. Extremal examples, which demonstrate that the bound is asymptotically sharp in all parameters, are furthermore provided.
The density of the set of sums
Théorie additive des nombres et problème de Waring
Théorie additive et géométrie des nombres