منابع مشابه
Small asymmetric sumsets in elementary abelian 2-groups
Let A and B be subsets of an elementary abelian 2-group G, none of which are contained in a coset of a proper subgroup. Extending onto potentially distinct summands a result of Hennecart and Plagne, we show that if |A + B| < |A| + |B|, then either A + B = G, or the complement of A + B in G is contained in a coset of a subgroup of index at least 8 (whence |A + B| ≥ 78 |G|). We indicate condition...
متن کاملGrowth of sumsets in abelian semigroups
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....
متن کاملPolynomial growth of sumsets in abelian semigroups
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 ...
متن کاملOn two questions about restricted sumsets in finite abelian groups
Let G be an abelian group of finite order n, and let h be a positive integer. A subset A of G is called weakly h-incomplete if not every element of G can be written as the sum of h distinct elements of A; in particular, if A does not contain h distinct elements that add to zero, then A is called weakly h-zero-sum-free. We investigate the maximum size of weakly hincomplete and weakly h-zero-sum-...
متن کاملOn Restricted Sumsets in Abelian Groups of Odd Order
Let G be an abelian group of odd order, and let A be a subset of G. For any integer h such that 2 ≤ h ≤ |A| − 2, we prove that |h∧A| ≥ |A| and equality holds if and only if A is a coset of some subgroup of G, where h∧A is the set of all sums of h distinct elements of A.
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1960
ISSN: 0001-5962
DOI: 10.1007/bf02546525