On the structure of sequences with forbidden zero-sum subsequences
Tom 98 / 2003
Colloquium Mathematicum 98 (2003), 213-222
MSC: Primary 11B75; Secondary 20K99.
DOI: 10.4064/cm98-2-7
Streszczenie
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 $c(3^a,3)=9.$
