Polynomial growth of sumsets in abelian semigroups
نویسندگان
چکیده
Let S be an abelian semigroup, and A a finite subset of S. The sumset hA consists of all sums of h elements of A, with repetitions allowed. Let |hA| denote the cardinality of hA. Elementary lattice point arguments are used to prove that an arbitrary abelian semigroup has polynomial growth, that is, there exists a polynomial p(t) such that |hA| = p(h) for all sufficiently large h. Lattice point counting is also used to prove that sumsets of the form h1A1 + · · ·+ hrAr have multivariate polynomial growth. 2000 Mathematics Subject Classification. Primary 11B13,11B75,11P21,20F65,20M14.
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