The cardinality of sumsets: different summands

• Autorzy: Brendan Murphy , Eyvindur Ari Palsson , Giorgis Petridis
• Języki publikacji: EN

Abstrakty

EN

We offer a complete answer to the following question on the growth of sumsets in commutative groups. Let h be a positive integer and $A, B₁, ..., B_h$ be finite sets in a commutative group. We bound $|A + B₁ + ... + B_h|$ 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.

Kategorie tematyczne

• 11P99: None of the above, but in this section
• 11B30: Arithmetic combinatorics; higher degree uniformity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 4
• Strony: 375-395

Daty

wydano

2015

Twórcy

autor

Brendan Murphy

• Department of Mathematics, University of Rochester, Rochester, NY 14627, U.S.A.

autor

Eyvindur Ari Palsson

• Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, U.S.A.

autor

Giorgis Petridis

• Department of Mathematics, University of Rochester, Rochester, NY 14627, U.S.A.

Identyfikatory

DOI

10.4064/aa167-4-4