On $\sum$-groups
نویسندگان
چکیده
منابع مشابه
On Zero-sum Partitions of Abelian Groups
In this paper, confirming a conjecture of Kaplan et al., we prove that every abelian group G, which is of odd order or contains exactly three involutions, has the zerosum-partition property. As a corollary, every tree with |G| vertices and at most one vertex of degree 2 is G-anti-magic.
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Let G be a finite abelian group with exponent n. Let s(G) denote the smallest integer l such that every sequence over G of length at least l has a zero-sum subsequence of length n. For p-groups whose exponent is odd and sufficiently large (relative to Davenport’s constant of the group) we obtain an improved upper bound on s(G), which allows to determine s(G) precisely in special cases. Our resu...
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Let G be a finite abelian group and k ∈ N with k exp(G). Then Ek(G) denotes the smallest integer l ∈ N such that every sequence S ∈ F(G) with |S| ≥ l has a zero-sum subsequence T with k |T |. In this paper we prove that if G = Cn1 ⊕ · · · ⊕ Cnr is a p-group, k ∈ N with k exp(G) and gcd(p, k) = 1, then Ek(G) = ⌊ k k − 1 r ∑
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Let G be a finite abelian group. A zero-sum problem on G asks for the smallest positive integer k such that for any sequence a1, . . . , ak of elements of G there exists a subsequence of required length the sum of whose terms vanishes. In this talk we will give a survey of problems and results in this field. In particular, we will talk about Olson’s theorem on the Davenport constanst of an abel...
متن کاملSome remarks on barycentric-sum problems over cyclic groups
We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer l such that each subset A of G with at least l elements contains a subset with k elements {g1, . . . , gk} satisfying g1 + · · ·+ gk = k gj for some 1 ≤ j ≤ k.
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 1964
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.1610