Plünnecke’s Inequality for Different Summands

  title={Plünnecke’s Inequality for Different Summands},
  author={Katalin Gyarmati and M{\'a}t{\'e} Matolcsi and Imre Z. Ruzsa},
The aim of this paper is to prove a general version of Plünnecke’s inequality. Namely, assume that for finite sets A, B1, . . . Bk we have information on the size of the sumsets A + Bi1 + · · · + Bil for all choices of indices i1, . . . il. 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 + B1 + · · · + Bk. As an application of this result we generalize an inequality of [1] concerning the submultiplicativity of cardinalities… CONTINUE READING