# The structure of a sequence with prescribed zero-sum subsequences

## Abstract

Let G be a finite additive abelian group. For a positive integer k, let s ≤ k(G) denote the smallest integer Ɩ such that every sequence of Ɩ elements from G (repetition allowed) has a nonempty zero-sum subsequence with length not exceeding k. The authors investigate the inverse problem of s≤D(G)-k(G) for the groups (Formula Presented), where D(G) denotes the Davenport constant of G. When n = pm > 5 for some prime p and positive integer m, (Formula Presented), and (Formula Presented), we solve the inverse problem.

## Publication Title

Integers

## Recommended Citation

Grynkiewicz, D., Wang, C., & Zhao, K.
(2020). The structure of a sequence with prescribed zero-sum subsequences.* Integers**, 20*, 1-31.
Retrieved from https://digitalcommons.memphis.edu/facpubs/5966