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تسجيل مستخدم جديدCharacteristic polynomials of Linial arrangements for exceptional root systems
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تأليف
Masahiko Yoshinaga
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The (extended) Linial arrangement $mathcal{L}_{Phi}^m$ is a certain finite truncation of the affine Weyl arrangement of a root system $Phi$ with a parameter $m$. Postnikov and Stanley conjectured that all roots of the characteristic 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 paper we prove that the conjecture is true for exceptional root systems when the parameter $m$ is sufficiently large. The proof is based on representations of the characteristic quasi-polynomials in terms of Eulerian polynomials.
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Let $q$ be a positive integer. In our recent paper, we proved that the cardinality of the complement of an integral arrangement, after the modulo $q$ reduction, is a quasi-polynomial of $q$, which we call the characteristic quasi-polynomial. In this
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