On the structure of sequences with forbidden zero-sum subsequences

Volume 98 / 2003

W. D. Gao, R. Thangadurai Colloquium Mathematicum 98 (2003), 213-222 MSC: Primary 11B75; Secondary 20K99. DOI: 10.4064/cm98-2-7


We study the structure of longest sequences in ${{\mathbb Z}}_n^d$ which have no zero-sum subsequence of length $n$ (or less). We prove, among other results, that for $n=2^a$ and $d $ arbitrary, or $n=3^a$ and $d=3$, every sequence of $c(n,d)(n-1)$ elements in ${{\mathbb Z}}_n^d$ which has no zero-sum subsequence of length $n$ consists of $c(n,d)$ distinct elements each appearing $n-1$ times, where $c(2^a,d)=2^d$ and $c(3^a,3)=9.$


  • W. D. GaoDepartment of Computer Science and Technology
    University of Petroleum
    Changping Shuiku Road
    Beijing 102200, China
  • R. ThangaduraiSchool of Mathematics
    Harish Chandra Research Institute
    Chhatnag Road, Jhusi
    Allahabad 211019, India

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