Geodesic
On subsequence sums of a zero-sum free sequence
The electronic journal of combinatorics, Tome 14 (2007)
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Let $G$ be a finite abelian group with exponent $m$, and let $S$ be a sequence of elements in $G$. Let $f(S)$ denote the number of elements in $G$ which can be expressed as the sum over a nonempty subsequence of $S$. In this paper, we show that, if $|S|=m$ and $S$ contains no nonempty subsequence with zero sum, then $f(S)\geq 2m-1$. This answers an open question formulated by Gao and Leader. They proved the same result with the restriction $(m,6)=1$.
DOI : 10.37236/970
Classification : 11B50 
@article{10_37236_970,
     author = {Fang Sun},
     title = {On subsequence sums of a zero-sum free sequence},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/970},
     zbl = {1206.11022},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/970/}
}
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Fang Sun. On subsequence sums of a zero-sum free sequence. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/970

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