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Upper bounds on the cardinality of higher sumsets

Volume 158 / 2013

Giorgis Petridis Acta Arithmetica 158 (2013), 299-319 MSC: Primary 11P99; Secondary 11B30. DOI: 10.4064/aa158-4-1


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 $h$.


  • Giorgis PetridisDepartment of Mathematics
    915 Hylan Building
    University of Rochester
    RC Box 270138
    Rochester NY 14627, U.S.A.

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