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On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths

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Gao W., Li Y., Zhao P., Zhuang J.

Colloquium Mathematicum

2016

tom 144

nr 1

31-44

Let G be an additive finite abelian group. For every positive integer ℓ, let $disc_{ℓ}(G)$ be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine $disc_{ℓ}(G)$ for certain finite groups, including cyclic groups, the groups $G = C₂ ⊕ C_{2m}$ and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum subsequences of distinct lengths. We shall prove that $disc(G) = max{disc_{ℓ}(G) | ℓ ≥ 1}$ and determine disc(G) for finite abelian p-groups G, where p ≥ r(G) and r(G) is the rank of G.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Gao W.

1 Li Y.

1 Zhao P.

1 Zhuang J.

1 2016

Wyniki wyszukiwania

On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths