# Inverse zero-sum problems II

@article{Schmid2008InverseZP, title={Inverse zero-sum problems II}, author={Wolfgang A. Schmid}, journal={arXiv: Number Theory}, year={2008} }

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…

## 36 Citations

Restricted inverse zero-sum problems in groups of rank 2

- Mathematics
- 2010

Let $(G,+)$ be a finite abelian group. Then, $\so(G)$ and $\eta(G)$ denote the smallest integer $\ell$ such that each sequence over $G$ of length at least $\ell$ has a subsequence whose terms sum to…

Inverse Zero-Sum Problems III: Addendum

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- 2021

The Davenport constant for a finite abelian group G is the minimal length l such that any sequence of l terms from G must contain a nontrivial zero-sum sequence. For the group G = (Z/nZ), its value…

Inverse zero-sum problems and algebraic invariants

- Mathematics
- 2008

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…

Long Zero-Sum Free Sequences over Cyclic Groups

- Mathematics, Biology
- 2013

The goal of this chapter is characterize the structure of those zero-sum free sequences close to the extremal possible length, and will be able to characterize this structure for sequences quite a ways away from the maximal value.

On the existence of zero-sum subsequences of distinct lengths

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- 2012

In this paper, we obtain a characterization of short normal sequences over a finite Abelian p-group, thus answering positively a conjecture of Gao for a variety of such groups. Our main result is…

On minimal product-one sequences of maximal length over Dihedral and Dicyclic groups

- Mathematics, Biology
- 2019

This work provides explicit characterizations of all minimal product- one sequences of length $\mathsf D (G)$ over Dihedral and Dicyclic groups and studies the unions of sets of lengths of the monoid of product-one sequences over these groups.

On the direct and inverse zero-sum problems over $C_n \rtimes_s C_2$

- Mathematics
- 2022

Let Cn be the cyclic group of order n. In this paper, we provide the exact values of some zero-sum constants over Cn⋊sC2 where s 6≡ ±1 (mod n), namely η-constant, Gao constant, and ErdősGinzburg-Ziv…

On the Davenport constant and on the structure of extremal zero-sum free sequences

- MathematicsPeriod. Math. Hung.
- 2012

It is shown that equality does not hold for C2 ⊕ C2nr, where n ≥ 3 is odd and r ≥ 4, and this gives new information on the structure of extremal zero-sum free sequences over C1nr.

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