Plunnecke's inequality for different summands

Katalin Gyarmati; Mate Matolcsi; Imre Z. Ruzsa

Plunnecke's inequality for different summands

Combinatorics 2008-10-09 v1 Commutative Algebra

Authors: Katalin Gyarmati , Mate Matolcsi , Imre Z. Ruzsa

Abstract

The aim of this paper is to prove a general version of Pl\"unnecke's inequality. Namely, assume that for finite sets $A$ , $B_1, ... B_k$ we have information on the size of the sumsets $A+B_{i_1}+... +B_{i_l}$ for all choices of indices $i_1, ... i_l.$ Then we prove the existence of a non-empty subset $X$ of $A$ such that we have `good control' over the size of the sumset $X+B_1+... +B_k$ . As an application of this result we generalize an inequality of \cite{gymr} concerning the submultiplicativity of cardinalities of sumsets.

Keywords

exponential sums inequalities divisor function

Cite

@article{arxiv.0810.1488,
  title  = {Plunnecke's inequality for different summands},
  author = {Katalin Gyarmati and Mate Matolcsi and Imre Z. Ruzsa},
  journal= {arXiv preprint arXiv:0810.1488},
  year   = {2008}
}

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8 pages

Plunnecke's inequality for different summands

Abstract

Keywords

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