Inverse zero-sum problems II

@article{Schmid2008InverseZP,
  title={Inverse zero-sum problems II},
  author={Wolfgang A. Schmid},
  journal={arXiv: Number Theory},
  year={2008}
}
  • W. Schmid
  • Published 24 January 2008
  • Mathematics
  • arXiv: Number Theory
Let $G$ be an additive finite abelian group. A sequence over $G$ is called a minimal zero-sum sequence if the sum of its terms is zero and no proper subsequence has this property. Davenport's constant of $G$ is the maximum of the lengths of the minimal zero-sum sequences over $G$. Its value is well-known for groups of rank two. We investigate the structure of minimal zero-sum sequences of maximal length for groups of rank two. Assuming a well-supported conjecture on this problem for groups of… 
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References

SHOWING 1-10 OF 44 REFERENCES
On short zero-sum subsequences. II.
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
Zero-sum problems in finite abelian groups and affine caps
For a finite abelian group G, let (G) denote the smallest integer l such that every sequence S over G of length | S| l has a zero-sum subsequence of length exp (G). We derive new upper and lower
Inverse zero-sum problems
Let G be an additive finite abelian group with exponent exp(G) = n. We define some central invariants in zero-sum theory: Let • D(G) denote the smallest integer l ∈ N such that every sequence S over
Inverse zero-sum problems III
Let G be a nite abelian group. The Davenport constant D(G) is the smallest integer ` 2 N such that every sequence S over G of length jSj ` has a nontrivial zero-sum subsequence. Let G = Cn Cn with n
MINIMAL ZERO-SUM SEQUENCES OF MAXIMUM LENGTH IN THE GROUP C3 ⊕ C3k
A sequence α in an additively written abelian group G is called a minimal zero-sum sequence if its sum is the zero element of G and none of its proper subsequences has sum zero. This note
The structure of maximal zero-sum free sequences
Let n be an integer, and consider finite sequences of elements of the group Z/nZ x Z/nZ. Such a sequence is called zero-sum free, if no subsequence has sum zero. It is known that the maximal length
On the index of minimal zero-sum sequences over finite cyclic groups
Inductive Methods and Zero-Sum Free Sequences
Abstract A fairly long-standing conjecture is that the Davenport constant of a group G = ℤ n 1 ⊕ ⋯ ⊕ ℤ nk with n 1 | ⋯ | nk is . This conjecture is false in general, but it remains to know for which
Two Zero-Sum Problems and Multiple Properties☆
Abstract In this paper we consider the following open problems: Conjecture  0.1. Let S be a sequence of 3 n −3 elements in C n ⊕ C n . If S contains no nonempty zero-sum subsequence of length not
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