The (extended) Linial arrangement $\mathcal{L}_{\Phi}^m$ is a certain finitetruncation of the affine Weyl arrangement of a root system $\Phi$ with aparameter $m$. Postnikov and Stanley conjectured that all roots of thecharacteristic polynomial of $\mathcal{L}_{\Phi}^m$ have the same real part,and this has been proved for the root systems of classical types. In this paperwe prove that the conjecture is true for exceptional root systems when theparameter $m$ is sufficiently large. The proof is based on representations ofthe characteristic quasi-polynomials in terms of Eulerian polynomials.
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机译：（扩展的）线性排列$ \ mathcal {L} _ {\ Phi} ^ m $是具有参数$ m $的根系统$ \ Phi $的仿射Weyl排列的确定截断。 Postnikov和Stanley推测$ \ mathcal {L} _ {\ Phi} ^ m $特征多项式的所有根都具有相同的实部，这已被经典类型的根系统证明。在本文中，我们证明了当参数$ m $足够大时，对于特殊的根系统该猜想是正确的。该证明基于欧拉多项式表示的特征拟多项式。
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