Plünnecke’s Inequality for Different Summands

Abstract

The aim of this paper is to prove a general version of Plünnecke's inequality. Namely, assume that for finite sets A, B 1 ,…,B k we have information on the size of the sumsets A+Bi 1+…+Bi 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 [1] concerning the submultiplicativity of cardinalities of sumsets.

Locations

• Bolyai Society mathematical studies - View
• arXiv (Cornell University) - View - PDF