Geodesic
Subsums of a zero-sum free subset of an abelian group
The electronic journal of combinatorics, Tome 15 (2008)
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Let $G$ be an additive finite abelian group and $S \subset G$ a subset. Let f$(S)$ denote the number of nonzero group elements which can be expressed as a sum of a nonempty subset of $S$. It is proved that if $|S|=6$ and there are no subsets of $S$ with sum zero, then f$(S)\geq 19$. Obviously, this lower bound is best possible, and thus this result gives a positive answer to an open problem proposed by R.B. Eggleton and P. Erdős in 1972. As a consequence, we prove that any zero-sum free sequence $S$ over a cyclic group $G$ of length $|S| \ge {6|G|+28\over19}$ contains some element with multiplicity at least ${6|S|-|G|+1\over17}$.
DOI : 10.37236/840
Classification : 11B75, 20K01
Mots-clés : additive finite abelian group, zero-sum free sequence, cyclic group 
@article{10_37236_840,
     author = {Weidong Gao and Yuanlin Li and Jiangtao Peng and Fang Sun},
     title = {Subsums of a zero-sum free subset of an abelian group},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/840},
     zbl = {1206.11015},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/840/}
}
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Weidong Gao; Yuanlin Li; Jiangtao Peng; Fang Sun. Subsums of a zero-sum free subset of an abelian group. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/840

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