منابع مشابه
Inverse zero-sum problems and algebraic invariants
— In this article, we study the maximal cross number of long zero-sumfree sequences in a finite Abelian group. Regarding this inverse-type problem, we formulate a general conjecture and prove, among other results, that this conjecture holds true for finite cyclic groups, finite Abelian p-groups and for finite Abelian groups of rank two. Also, the results obtained here enable us to improve, via ...
متن کاملInverse Zero - Sum Problems Ii Wolfgang
Let G denote a finite abelian group. The Davenport constant D(G) is the smallest integer such that each sequence over G of length at least D(G) has a non-empty zero-sum subsequence, i.e., the sum of the terms equals 0 ∈ G. The constants s(G) and η(G) are defined similarly; the additional condition that the length of the zero-sum subsequence is equal to (not greater than, resp.) the exponent of ...
متن کاملInverse zero-sum problems in finite Abelian p-groups
— In this paper, we study the minimal number of elements of maximal order within a zero-sumfree sequence in a finite Abelian p-group. For this purpose, in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, the method that we use here enables us to show that, if we ...
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...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2007
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa128-3-5