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Writing the fully color dressed and graviton amplitudes, respectively, as ${\bf A}=<C|A> =<C|M|N> $ and ${\bf A}_{gr}= <\tilde N|M|N> $, where $|A> $ is a set of Kleiss-Kuijf color-ordered basis, $|N>, $|\tilde N> $ and $|C>$ are the similarly ordered numerators and color coefficients, we show that the propagator matrix $M$ has $(n-3)(n-3)!$ independent eigenvectors $|\lambda ^0_j>$ with zero eigenvalue, for $n$-particle processes.
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S. Stieberger, “Open & Closed vs. Pure Open String Disk Amplitudes,” arXiv:0907.2211 [hep-th]
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