Sums of dilates

Authors:
Boris Bukh
Affiliations:
Department of mathematics, fine hall, washington road, princeton, nj 08544-1000, usa (e-mail: bbukh@math.princeton.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2008

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Abstract

The λ-dilate of a set A is λċA={λa : a∈A}. We give an asymptotically sharp lower bound on the size of sumsets of the form λ1ċA+ċċċ+λkċA for arbitrary integers λ1,. . .,λk and integer sets A. We also establish an upper bound for such sums, which is similar to, but often stronger than Plünnecke's inequality.