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

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

2010-09-29

arxiv.org/abs/1009.5835v1

Mathematics

Combinatorics

The final publication will be availabe via http://www.springerlink.com

Scientific paper

Let $G = C_{n_1} \oplus ... \oplus C_{n_r}$ with $1 < n_1 \t ... \t n_r$ be a finite abelian group, $\mathsf d^* (G) = n_1 + ... + n_r - r$, and let $\mathsf d (G)$ denote the maximal length of a zero-sum free sequence over $G$. Then $\mathsf d (G) \ge \mathsf d^* (G)$, and the standing conjecture is that equality holds for $G = C_n^r$. We show that equality does not hold for $C_2 \oplus C_{2n}^r$, where $n \ge 3$ is odd and $r \ge 4$. This gives new information on the structure of extremal zero-sum free sequences over $C_{2n}^r$.

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