Zero-sum-free sequences with few subsequence sums

TL;DR

This paper proves that zero-sum-free sequences in abelian groups typically have at least twice as many distinct subsequence sums as their length, unless they have a specific rigid structure.

Contribution

It establishes a lower bound on the number of distinct subsequence sums for zero-sum-free sequences, characterizing the structure when the bound is not met.

Findings

Zero-sum-free sequences of length n have at least 2n distinct subsequence sums.

Sequences with fewer than 2n sums have a rigid, well-defined structure.

The result characterizes the structure of sequences with minimal subsequence sums.

Abstract

We show that a zero-sum-free sequence of length $n$ over an abelian group spans at least $2n$ distinct subsequence sums, unless it possesses a rigid, easily-described structure.