Chi, Rui; Ding, Shuyan; Gao, Weidong; Geroldinger, A.; Schmid, W. A. On zero-sum subsequences of restricted size. IV. (English) Zbl 1090.11014 Acta Math. Hung. 107, No. 4, 337-344 (2005). For a finite abelian group \(G\) the invariant \(s(G)\) (resp. the invariant \(s_0(G)\)) is the smallest integer \(\ell\in \mathbb N\) such that every sequence \(S\) in \(G\) of length \(| S| \geq \ell \) has a subsequence \(T\) with sum zero and length \(| T| =\exp(G)\) (resp. length \(| T| \equiv \bmod \exp(G)\)). The Davenport constant \(D(G)\) of \(G\) is the smallest integer \(\ell\in \mathbb N\) such that every sequences \(S\) in \(G\) with length \(| S| \geq \ell\) contains a zero-sum subsequence. For every \(n\in \mathbb N\) is denoted by \(C_n\) a cyclic group with \(n\) elements. The main result of this article is the following theorem: Let \(m,n\in \mathbb N\) with \(n\geq \frac 13 (m^2-m+1)\). If \(s_0(C^2_m)=3m-2\) and \(D(C^3_n)=3n-2\), then \(s_0(C^2_{mn})=3mn-2\).For the first three parts, see J. Number Theory 61, No. 1, 97–102 (1996; Zbl 0870.11016), Discrete Math. 271, No. 1-3, 51–59 (2003; Zbl 1089.11012) and Ars Comb. 61, 65–72 (2001; Zbl 1101.11311). Reviewer: Erich Härtter (Mainz) Cited in 2 ReviewsCited in 10 Documents MSC: 11B75 Other combinatorial number theory 20K01 Finite abelian groups 11B50 Sequences (mod \(m\)) Keywords:zero-sum sequence; finite abelian groups Citations:Zbl 1101.11311; Zbl 0870.11016; Zbl 1089.11012 PDFBibTeX XMLCite \textit{R. Chi} et al., Acta Math. Hung. 107, No. 4, 337--344 (2005; Zbl 1090.11014) Full Text: DOI