Upper Bounds on the Cardinality of Higher Sumsets
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boundupperboundscardinalitycommutativedecreasesexistingfactor
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Let A and B be finite sets in a commutative group. We bound |A+hB| in terms of |A|, |A+B| and h. We provide a submultiplicative upper bound that improves on the existing bound of Imre Ruzsa by inserting a factor that decreases with h.
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