Sums of dilates
Number Theory
2008-04-03 v3 Combinatorics
Abstract
The lambda-dilate of a set A is lambda*A={lambda a : a \in A}. We give an asymptotically sharp lower bound on the size of sumsets of the form lambda_1*A+...+lambda_k*A for arbitrary integers lambda_1,...,lambda_k and integer sets A. We also establish an upper bound for such sums, which is similar to, but often stronger than Plunnecke's inequality.
Cite
@article{arxiv.0711.1610,
title = {Sums of dilates},
author = {Boris Bukh},
journal= {arXiv preprint arXiv:0711.1610},
year = {2008}
}
Comments
14 pages, typos and small errors fixed