The subsums of zero-sum free sequences in finite cyclic groups

Let ${\mathbb{Z}}_n$ be the cyclic group of order $n\ge 3$ additively written. S. Savchev & F. Chen (2007) proved that for each zero-sum free sequence $S = a_1 \bullet \dots \bullet a_t$over$\mathbb Z_n$oflength$t > n/2$, there is an integer $g$ coprime to $n$ such that, if $\bar{r}$ denotes the least positive integer in the congruence class $r$ modulo $n$, then $\sum_{i=1}^t \overline{ga_i} < n$\mathrm{.}Underthesamehypothesis,inthispaperweshowthat$$\left{ \sum_{i \in \Lambda} \overline{ga_i} ;; \Bigg| ;; \Lambda \subset {1,2,\dots,t} \right} = \left{ 1, 2, \dots, \sum_{i=1}^t \overline{ga_i}\right}.$$ It simplifies many calculations on inverse zero-sum problems.