Upper bounds on the cardinality of higher sumsets
Volume 158 / 2013
Acta Arithmetica 158 (2013), 299-319
MSC: Primary 11P99; Secondary 11B30.
DOI: 10.4064/aa158-4-1
Abstract
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 $h$.
