منابع مشابه
A Survey of Zero-sum Problems on Abelian Groups
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 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...
متن کاملContributions to zero-sum problems
A prototype of zero–sum theorems, the well–known theorem of Erdős, Ginzburg and Ziv says that for any positive integer n, any sequence a1, a2, · · · , a2n−1 of 2n − 1 integers has a subsequence of n elements whose sum is 0 modulo n. Appropriate generalizations of the question, especially that for (Z/pZ), generated a lot of research and still have challenging open questions. Here we propose a ne...
متن کاملA Unified Theory of Zero - Sum Problems
Abstract. In combinatorial number theory, zero-sum problems, subset sums and covers of the integers are three different topics initiated by P. Erdős and investigated by many researchers; they play important roles in both number theory and combinatorics. In this paper we reveal some deep connections among these seemingly unrelated fascinating areas, and establish a unified theory for the first t...
متن کاملBarycentric-sum problems: a survey
Let G be a finite abelian group. A sequence in G is barycentric if it contains one element “average” of its terms. We give a survey of results and open problems concerning sufficient conditions for the existence of barycentric sequences. Moreover values and open problems on the k-barycentric Davenport constant BD(k, G), the barycentric Davenport constant BD(G), the strong k-barycentric Davenpor...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00308-6