On the number of subsequences with a given sum in a finite abelian group
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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 $N_g(S)\ge2^{|S|-D(G)+1}$, 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.
@article{10_37236_620,
author = {Gerard Jennhwa Chang and Sheng-Hua Chen and Yongke Qu and Guoqing Wang and Haiyan Zhang},
title = {On the number of subsequences with a given sum in a finite abelian group},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/620},
zbl = {1293.11045},
url = {http://geodesic.mathdoc.fr/articles/10.37236/620/}
}
TY - JOUR AU - Gerard Jennhwa Chang AU - Sheng-Hua Chen AU - Yongke Qu AU - Guoqing Wang AU - Haiyan Zhang TI - On the number of subsequences with a given sum in a finite abelian group JO - The electronic journal of combinatorics PY - 2011 VL - 18 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.37236/620/ DO - 10.37236/620 ID - 10_37236_620 ER -
%0 Journal Article %A Gerard Jennhwa Chang %A Sheng-Hua Chen %A Yongke Qu %A Guoqing Wang %A Haiyan Zhang %T On the number of subsequences with a given sum in a finite abelian group %J The electronic journal of combinatorics %D 2011 %V 18 %N 1 %U http://geodesic.mathdoc.fr/articles/10.37236/620/ %R 10.37236/620 %F 10_37236_620
Gerard Jennhwa Chang; Sheng-Hua Chen; Yongke Qu; Guoqing Wang; Haiyan Zhang. On the number of subsequences with a given sum in a finite abelian group. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/620
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