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• # Artykuł - szczegóły

## Colloquium Mathematicum

2016 | 144 | 1 | 31-44

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

EN

### Abstrakty

EN
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.

31-44

wydano
2016

### Twórcy

autor
• Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P.R. China
autor
• Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1
autor
• Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P.R. China
autor
• Department of Mathematics, Dalian Maritime University, Dalian 116024, P.R. China