Some inverse problems in zero-sum theory
The author proves five main results about some special sequences over \(\mathbb{Z} / n \mathbb{Z}\). The simplest result reads as follows: Theorem. Let \(r,n\) be positive integers. Assume that \(n \geq 4\). If a sequence \(S\) of length \((r+1)n-2\) over \(\mathbb{Z} / n \mathbb{Z}\) does not have any \(r n\)-length zero-sum subsequence, then \(S\) contains two elements of \(\mathbb{Z} / n \mathbb{Z}\) such that one of them occurs \((r-1) n -1\) times and the other element occurs \((i+1) n -1\) times, for some \(i \in \{0,1,\ldots,r-1\}\).
scientific article; zbMATH DE number 7625374
scientific article