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

Weidong GaoYuanlin LiPingping ZhaoJujuan Zhuang — 2016

Colloquium Mathematicae

Let G be an additive finite abelian group. For every positive integer ℓ, let d i s c ( 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 d i s c ( G ) for certain finite groups, including cyclic groups, the groups G = C C 2 m 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...

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