منابع مشابه
Remarks on Tiny Zero - Sum Sequences
Let G be an additive finite abelian group with exponent exp(G). Let S = g1 · . . . · gl be a sequence over G and k(S) = ord(g1)+· · ·+ord(gl) be its cross number. Let η(G) (resp. t(G)) be the smallest integer t such that every sequence of t elements (repetition allowed) from G contains a non-empty zero-sum subsequence T of length |T | ≤ exp(G) (resp. k(T ) ≤ 1). It is easy to see that t(G) ≥ η(...
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In a recent paper E. J. McShane [3]2 has given a theorem which is the common core of a variety of results about Baire sets, Baire functions, and convex sets in topological spaces including groups and linear spaces. In general terms his theorem states that if J is a family of open maps defined in one topological space Xi into another, X2, the total image JiS) of a second category Baire set S in ...
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For a graph H with at most n vertices and a weighing of the edges of Kn with integers, we seek a copy of H in Kn whose weight is minimal, possibly even zero. Of a particular interest are the cases where H is a spanning subgraph (or an almost spanning subgraph) and the case where H is a fixed graph. In particular, we show that relatively balanced weighings of Kn with {−r, . . . , r} guarantee al...
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Abstract. Let G be a finite abelian group, and let η(G) be the smallest integer d such that every sequence over G of length at least d contains a zero-sum subsequence T with length |T | ∈ [1, exp(G)]. In this paper, we investigate the question whether all non-cyclic finite abelian groups G share with the following property: There exists at least one integer t ∈ [exp(G)+1, η(G)− 1] such that eve...
متن کاملOn Zero - Sum Problems
Let G be an additive abelian group. The zero-sum problem for G asks for the least positive integer k such that for any a1, · · · , ak ∈ G there is an I ⊆ {1, · · · , k} of required cardinality satisfying ∑ i∈I ai = 0. In this talk we will introduce the famous theorem of P. Erdős, A. Ginzburg and A. Ziv (for G = Zn), and recent results of L. Rónya on the Kemnitz conjecture concerning the group Z...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1996
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0108