1Department of Mathematics University of Rochester Rochester, NY 14627, U.S.A. 2Department of Mathematics and Statistics Williams College Williamstown, MA 01267, U.S.A.
Acta Arithmetica, Tome 167 (2015) no. 4, pp. 375-395
We offer a complete answer to the following question on the growth of sumsets in commutative groups. Let $h$ be a positive integer and $A, B_1, \dots , B_h$ be finite sets in a commutative group. We bound $|A+B_1+\dots +B_h|$ 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 parameters, are furthermore provided.
1
Department of Mathematics University of Rochester Rochester, NY 14627, U.S.A.
2
Department of Mathematics and Statistics Williams College Williamstown, MA 01267, U.S.A.
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author = {Brendan Murphy and Eyvindur Ari Palsson and Giorgis Petridis},
title = {The cardinality of sumsets: different summands},
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Brendan Murphy; Eyvindur Ari Palsson; Giorgis Petridis. The cardinality of sumsets: different summands. Acta Arithmetica, Tome 167 (2015) no. 4, pp. 375-395. doi: 10.4064/aa167-4-4
