Inverse Zero-Sum Problems III
| dc.creator | Gao, Weidong | |
| dc.creator | Geroldinger, Alfred | |
| dc.creator | Grynkiewicz, David J. | |
| dc.date | 2008-01-24 | |
| dc.date.accessioned | 2026-07-07T08:56:13Z | |
| dc.date.available | 2026-07-07T08:56:13Z | |
| dc.description | Let $G$ be a finite abeilian group. A sequence $S$ with terms from $G$ is zero-sum if the sum of terms in $S$ equals zero. It is a minimal zero-sum sequence if no proper, nontrivial subsequence is zero-sum. The maximal length of a minimal zero-sum subsequence in $G$ is the Davenport constant, denoted $D(G)$. For a rank 2 group $G=C_n \oplus C_n$, it is known that $D(G)=2n-1$. However, the structure of all maximal length minimal zero-sum sequences remains open. If every such sequence contains a term with multiplicity $n-1$, then $C_n \oplus C_n$ is said to have Property B, and it is conjectured that this is true for all rank 2 groups $C_n \oplus C_n$. In this paper, we show that Property B is multiplicative, namely, if $G=C_n \oplus C_n$ and $G=C_m \oplus C_m$ both satisfy Property B, with $m, n\geq 3$ odd and $mn>9$, then $C_{mn}\oplus C_{mn}$ satisfies Property B also. Combined with previous work in the literature, this reduces the question of establishing Property B to the prime cases, and in such case the complete structural description of the sequence follows. | |
| dc.identifier | https://arxiv.org/abs/0801.3792 | |
| dc.identifier | http://arxiv.org/abs/0801.3792 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146533 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11BP70;11B50;11B75 | |
| dc.title | Inverse Zero-Sum Problems III | |
| dc.type | text |