Davenport constant with weights

Details Davenport constant with weights Davenport constant with weights

2009-09-13

arxiv.org/abs/0909.2388v1

Mathematics

Number Theory

6pages

Scientific paper

For the cyclic group $G=\mathbb{Z}/n\mathbb{Z}$ and any non-empty $A\in\mathbb{Z}$. We define the Davenport constant of $G$ with weight $A$, denoted by $D_A(n)$, to be the least natural number $k$ such that for any sequence $(x_1, ..., x_k)$ with $x_i\in G$, there exists a non-empty subsequence $(x_{j_1}, ..., x_{j_l})$ and $a_1, ..., a_l\in A$ such that $\sum_{i=1}^l a_ix_{j_i} = 0$. Similarly, we define the constant $E_A(n)$ to be the least $t\in\mathbb{N}$ such that for all sequences $(x_1, >..., x_t)$ with $x_i \in G$, there exist indices $j_1, ..., j_n\in\mathbb{N}, 1\leq j_1 <... < j_n\leq t$, and $\vartheta_1, >..., \vartheta_n\in A$ with $\sum^{n}_{i=1} \vartheta_ix_{j_i} = 0$. In the present paper, we show that $E_A(n)=D_A(n)+n-1$. This solve the problem raised by Adhikari and Rath \cite{ar06}, Adhikari and Chen \cite{ac08}, Thangadurai \cite{th07} and Griffiths \cite{gr08}.

Affiliated with

Also associated with

No associations

Rating

Davenport constant with weights does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Davenport constant with weights, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Davenport constant with weights will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-628545