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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## 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 $c(3^a,3)=9.$

#### Autorzy

• W. D. GaoDepartment of Computer Science and Technology
University of Petroleum
Beijing 102200, China
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