Characteristic polynomials of Linial arrangements for exceptional root systems

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:157

Article

Yoshinaga, Masahiko¹ 

[1] Hokkaido Univ, Dept Math, Kita Ku, North 10,West 8, Sapporo, Hokkaido 0600810, Japan

关键词: Hyperplane arrangements;    Linial arrangements;    Characteristic polynomials;   

DOI  :  10.1016/j.jcta.2018.02.011

来源: Elsevier

【 摘 要 】

The (extended) Linial arrangement L-Phi(m) is a certain finite truncation of the affine Weyl arrangement of a root system with a parameter m. Postnikov and Stanley conjectured that all roots of the characteristic polynomial of 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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