Subsequence Sums of Zero-sum free Sequences II

Let $G$ be a finite abelian group, and let $S$ be a sequence over $G$. Let $f(S)$ denote the number of elements in $G$ which can be expressed as the sum over a nonempty subsequence of $S$. In this paper, we determine all the sequences $S$ that contains no zero-sum subsequences and $f(S)\leq 2|S|-1$.Comment: 11page

Subsequence Sums of Zero-sum-free Sequences

Let G be a finite abelian group, and let S be a sequence of elements in G. Let f(S) denote the number of elements in G which can be expressed as the sum over a nonempty subsequence of S. In this paper, we slightly improve some results of [10] on f(S) and we show that for every zero-sum-free sequences S over G of length |S | = exp(G) + 2 satisfying f(S) � 4exp(G) − 1. Key words: Zero-sum problems, Davenport’s constant, zero-sum-free sequence.