The Cardinality of Sumsets: Different Summands

Brendan Murphy, Eyvindur Ari Palsson, Giorgis Petridis

Research output: Contribution to journalArticle (Academic Journal)peer-review


Let $h$ be a positive integer and $A, B_1, B_2,\dots, B_h$ be finite sets in a commutative group. We bound $|A+B_1+...+B_h|$ from above in terms of $|A|, |A+B_1|,\dots,|A+B_h|$ and $h$. Extremal examples, which demonstrate that the bound is asymptotically sharp in all the parameters, are furthermore provided.
Original languageEnglish
JournalActa Arithmetica
Publication statusPublished - 9 Sep 2013

Bibliographical note

25 pages. A minor change in the statement of Lemma 5.13


  • math.CO
  • 11B30

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