On the number of subsequences with a given sum in a finite abelian group

Details On the number of subsequences with a given sum in a finite abelian group On the number of subsequences with a given sum in a finite abelian group

2011-01-24

arxiv.org/abs/1101.4492v1

Mathematics

Combinatorics

9 pages

Scientific paper

Suppose $G$ is a finite abelian group and $S$ is a sequence of elements in $G$. For any element $g$ of $G$, let $N_g(S)$ denote the number of subsequences of $S$ with sum $g$. The purpose of this paper is to investigate the lower bound for $N_g(S)$. In particular, we prove that either $N_g(S)=0$ or $N_g(S) \ge 2^{|S|-D(G)+1}$, where $D(G)$ is the smallest positive integer $\ell$ such that every sequence over $G$ of length at least $\ell$ has a nonempty zero-sum subsequence. We also characterize the structures of the extremal sequences for which the equality holds for some groups.

Affiliated with

Also associated with

No associations

Rating

On the number of subsequences with a given sum in a finite abelian group 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 On the number of subsequences with a given sum in a finite abelian group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the number of subsequences with a given sum in a finite abelian group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-636660