The Cardinality of Sumsets: Different Summands
Abstract
Let h be a positive integer and A, B1, B2,…, 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 the parameters, are furthermore provided.
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