Plunnecke's inequality for different summands
Abstract
The aim of this paper is to prove a general version of Pl\"unnecke'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 gymr concerning the submultiplicativity of cardinalities of sumsets.
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