\documentclass[12pt]{article}
\usepackage{amsmath,mathrsfs,bbm}
\usepackage{amssymb}
\textwidth=4.825in
\overfullrule=0pt
\thispagestyle{empty}

\begin{document}
\noindent
%
%
{\bf Gerard Jennhwa Chang, Sheng-Hua Chen, Yongke Qu, Guoqing Wang and Haiyan Zhang}
%
%

\medskip
\noindent
%
%
{\bf On the Number of Subsequences with a Given Sum in a Finite Abelian Group}
%
%

\vskip 5mm
\noindent
%
%
%
%
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.



\end{document}

.
