English

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.

Keywords

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

R2 v1 2026-06-21T09:42:11.046Z