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A counterexample to a conjecture of Erdős, Graham and Spencer
The electronic journal of combinatorics, Tome 15 (2008)
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It is conjectured by Erdős, Graham and Spencer that if $1 \leq a_1 \leq a_2 \leq \cdots \leq a_s$ with $\sum_{i=1}^s 1/a_i < n - 1/30$, then this sum can be decomposed into $n$ parts so that all partial sums are $\leq 1$. In this note we propose a counterexample which gives a negative answer to this conjecture.
DOI : 10.37236/918
Classification : 11B75
Mots-clés : Erdős-Graham-Spencer conjecture, Erdős problem, partition 
@article{10_37236_918,
     author = {Song Guo},
     title = {A counterexample to a conjecture of {Erd\H{o}s,} {Graham} and {Spencer}},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/918},
     zbl = {1206.11033},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/918/}
}
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Song Guo. A counterexample to a conjecture of Erdős, Graham and Spencer. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/918

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