Question. Let $a_1,...a_n\in\{0,1,-1\}^m$ and $\sum a_i=(1,...,1)$. Is there a permutation $\tau$ of $\{1,...,n\}$ Such that for each $k\in \{1,...,n\}$ the vector $\sum_{i=1}^k a_{\tau (i)}$ has entries greater or equal than -1?
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I have proved a similar problem using Gordan's Theorem and I think this one has also the same way to answer, but I have not find it yet. Any way I would appreciate any answer you can give. – Golab Jun 28 '15 at 05:24