On the structure of n-zero-sum free sequences over cyclic groups of order n

Abstract

Let G be a finite cyclic group of order n. The Erdős–Ginzburg–Ziv theorem states that each sequence of length 2n - 1 over G has a zero-sum subsequence of length n. A sequence without a zero-sum subsequence of length n is called n-zero-sum free. Savchev and Chen characterized all the n-zero-sum free sequences of length n + k - 1 over G, where [Formula: see text]. In the present paper, we determine all the n-zero-sum free sequences of length [Formula: see text] over G.