Geodesic
The cardinality of sumsets: different summands
Brendan Murphy 1   ; Eyvindur Ari Palsson 2   ; Giorgis Petridis 1
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.
Acta Arithmetica, Tome 167 (2015) no. 4, pp. 375-395 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa167-4-4
Keywords: offer complete answer following question growth sumsets commutative groups positive integer dots finite sets commutative group bound dots above terms dots extremal examples which demonstrate bound asymptotically sharp parameters furthermore provided

Brendan Murphy  1   ; Eyvindur Ari Palsson  2   ; Giorgis Petridis  1

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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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

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