Long zero-free sequences in finite cyclic groups

A sequence in an additively written abelian group is called zero-free if each of its nonempty subsequences has sum different from the zero element of the group. The article determines the structure of the zero-free sequences with lengths greater than n/2n/2 in the additive group ZnZn of integers modulo n. The main result states that for each zero-free sequence (ai)i=1ℓ of length ℓ>n/2ℓ>n/2 in ZnZn there is an integer g coprime to n   such that if gai¯ denotes the least positive integer in the congruence class gaigai (modulo n  ), then Σi=1ℓgai¯