Subsums of a Zero-sum Free Subset of an Abelian Group
نویسندگان
چکیده
منابع مشابه
Subsums of a Zero-sum Free Subset of an Abelian Group
Let G be an additive finite abelian group and S ⊂ G a subset. Let f(S) denote the number of nonzero group elements which can be expressed as a sum of a nonempty subset of S. It is proved that if |S| = 6 and there are no subsets of S with sum zero, then f(S) ≥ 19. Obviously, this lower bound is best possible, and thus this result gives a positive answer to an open problem proposed by R.B. Egglet...
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A subset A of a given finite abelian group G is called (k, l)-sum-free if the sum of k (not necessarily distinct) elements of A does not equal the sum of l (not necessarily distinct) elements of A. We are interested in finding the maximum size λk,l(G) of a (k, l)-sum-free subset in G. A (2, 1)-sum-free set is simply called a sum-free set. The maximum size of a sum-free set in the cyclic group Z...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/840