Plünnecke’s Inequality for Different Summands
نویسنده
چکیده
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 of sumsets.
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