The cardinality of sumsets: different summands
Brendan Murphy ; Eyvindur Ari Palsson ; Giorgis Petridis
Acta Arithmetica, Tome 168 (2015), p. 375-395 / Harvested from The Polish Digital Mathematics Library
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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,B₁,...,Bh be finite sets in a commutative group. We bound |A+B₁+...+Bh| from above in terms of |A|, |A + B₁|, ..., |A+Bh| and h. Extremal examples, which demonstrate that the bound is asymptotically sharp in all parameters, are furthermore provided.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:279673 
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     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 168 (2015) pp. 375-395. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-4-4/