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The automorphism group of some semigroups

Richard Byrd, Justin Lloyd, Franklin Pederson, James Stepp (1984)

Fundamenta Mathematicae

The cardinality of sumsets: different summands

Brendan Murphy, Eyvindur Ari Palsson, Giorgis Petridis (2015)

Acta Arithmetica

We offer a complete answer to the following question on the growth of sumsets in commutative groups. Let h be a positive integer and $A, B ₁, . . ., B_{h}$ be finite sets in a commutative group. We bound $| A + B ₁ + . . . + B_{h} |$ from above in terms of |A|, |A + B₁|, ..., $| A + B_{h} |$ 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

Imre Ruzsa (1991)

Acta Arithmetica

Théorie additive des nombres et problème de Waring

François Dress (1970/1971)

Séminaire de théorie des nombres de Bordeaux

Théorie additive et géométrie des nombres

Jean-Marc DESHOUILLERS (1980/1981)

Seminaire de Théorie des Nombres de Bordeaux