Growth of sumsets in abelian semigroups
نویسنده
چکیده
Let S be an abelian semigroup, written additively, that contains the identity element 0. Let A be a nonempty subset of S. The cardinality of A is denoted |A|. For any positive integer h, the sumset hA is the set of all sums of h not necessarily distinct elements of A. We define hA = {0} if h = 0. Let A1, . . . , Ar, and B be nonempty subsets of S, and let h1, . . . , hr be nonnegative integers. We denote by B + h1A1 + · · ·+ hrAr (1)
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تاریخ انتشار 2008