1Department of Computer Science and Technology University of Petroleum Changping Shuiku Road Beijing 102200, China 2School of Mathematics Harish Chandra Research Institute Chhatnag Road, Jhusi Allahabad 211019, India
Colloquium Mathematicum, Tome 98 (2003) no. 2, pp. 213-222
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 $c(3^a,3)=9.$
Keywords:
study structure longest sequences mathbb which have zero sum subsequence length prove among other results arbitrary every sequence n elements mathbb which has zero sum subsequence length consists distinct elements each appearing n times where
Affiliations des auteurs :
W. D. Gao
1
;
R. Thangadurai
2
1
Department of Computer Science and Technology University of Petroleum Changping Shuiku Road Beijing 102200, China
2
School of Mathematics Harish Chandra Research Institute Chhatnag Road, Jhusi Allahabad 211019, India
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W. D. Gao; R. Thangadurai. On the structure of sequences with
forbidden zero-sum subsequences. Colloquium Mathematicum, Tome 98 (2003) no. 2, pp. 213-222. doi: 10.4064/cm98-2-7
