# 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

### Inverse zero-sum problems and algebraic invariants

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- 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…

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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 Olson and the Strong Davenport constants

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A subset $S$ of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of $S$ is non-zero. We investigate the maximal cardinality of…

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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.

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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…

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- 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.

### The Inverse Problem Associated to the Davenport Constant for C2+C2+C2n, and Applications to the Arithmetical Characterization of Class Groups

- MathematicsElectron. J. Comb.
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A characterization, via the system of sets of lengths, of the class group of rings of algebraic integers is obtained for certain types of groups, and the Davenport constants of groups of the form C 4 ⊕ C4n and C 6 ⊵ C6n are determined.

### Structure of long idempotent-sum-free sequences over finite cyclic semigroups

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- 2020

Let $\mathcal{S}$ be a finite cyclic semigroup written additively. An element $e$ of $\mathcal{S}$ is said to be idempotent if $e+e=e$. A sequence $T$ over $\mathcal{S}$ is called {\sl idempotent-sum…

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