Subsequence Sums of Zero-sum free Sequences II

TL;DR

This paper characterizes zero-sum free sequences over finite abelian groups with a bounded number of representable sums, extending understanding of subsequence sum structures.

Contribution

It determines all zero-sum free sequences with a limited number of sum representations, advancing the classification of such sequences in finite abelian groups.

Findings

Identifies all sequences with no zero-sum subsequences and f(S) ≤ 2|S|-1.

Provides a complete characterization of these sequences.

Extends previous results on subsequence sums in abelian groups.

Abstract

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 $f(S)\leq 2|S|-1$.