LAUSR

Abstract The article characterizes the minimal zero-sum sequences over the cyclic group C n with lengths between ⌊ n / 3 ⌋ + 3 and ⌊ n / 2 ⌋ + 1 , for n ≥ 10 . This is a step beyond established results about minimal zero-sum sequences over C n of lengths at least ⌊ n / 2 ⌋ + 2 . The range of the obtained characterization is optimal. Among the possible approaches we choose one with a strong emphasis on unsplittable sequences—intriguing objects generalizing the longest minimal zero-sum sequences over an abelian group. The unsplittable sequences over C n with lengths in [ ⌊ n / 3 ⌋ + 3 , ⌊ n / 2 ⌋ + 1 ] prove capable of capturing the essence of our setting and deserve an explicit description.