Optimally small sumsets in finite abelian groups
نویسندگان
چکیده
منابع مشابه
On 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-...
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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...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2003
ISSN: 0022-314X
DOI: 10.1016/s0022-314x(03)00060-x