An inverse problem about minimal zero-sum sequences over finite cyclic groups

Abstract

The article characterizes the minimal zero-sum sequences over the cyclic group Cn 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 Cn 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 Cn with lengths in [⌊n/3⌋+3,⌊n/2⌋+1] prove capable of capturing the essence of our setting and deserve an explicit description.