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On the inverse problems associated with subsequence sums of zero-sum free sequences over finite abelian groups

Volume 163 / 2021

Jiangtao Peng, Yuanlin Li, Chao Liu, Meiling Huang Colloquium Mathematicum 163 (2021), 317-332 MSC: Primary 11P70; Secondary 11B75. DOI: 10.4064/cm8033-12-2019 Published online: 31 August 2020

Abstract

Let $G$ be an additive finite abelian group with exponent $\exp (G)$ and $S$ be a sequence of elements of $G$. Let $\Sigma (S) \subset G$ denote the set of group elements which can be expressed as the sum of a nonempty subsequence of $S$. We say $S$ is zero-sum free if $0 \not \in \Sigma (S)$. Suppose $S$ is a zero-sum free sequence of $G$ of length $|S|=\exp (G)+k$, where $k \in \{0,1\}$. It was proved by F. Sun and W. Gao et al. that $|\Sigma (S)|\geq (k+2)\exp (G)-1$. In this paper, we determine the structure of the zero-sum free sequences $S$ such that $|S|=\exp (G)+k$ and $|\Sigma (S)|=(k+2)\exp (G)-1$ for $k\in \{0,1\}$.

Authors

  • Jiangtao PengCollege of Science
    Civil Aviation University of China
    Tianjin 300300, P.R. China
    e-mail
  • Yuanlin LiDepartment of Mathematics and Statistics
    Brock University
    St. Catharines, Ontario, Canada L2S 3A1
    e-mail
  • Chao LiuDepartment of Mathematics and Statistics
    Brock University
    St. Catharines, Ontario, Canada L2S 3A1
    e-mail
  • Meiling HuangDepartment of Mathematics and Statistics
    Brock University
    St. Catharines, Ontario, Canada L2S 3A1
    e-mail

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