Sums of dilates
Abstract
The lambda-dilate of a set A is lambda*A=lambda a : a ∈ A. We give an asymptotically sharp lower bound on the size of sumsets of the form lambda1*A+...+lambdak*A for arbitrary integers lambda1,...,lambdak and integer sets A. We also establish an upper bound for such sums, which is similar to, but often stronger than Plunnecke's inequality.
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