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Characteristic polynomials of Linial arrangements for exceptional root systems
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| Title: | Characteristic polynomials of Linial arrangements for exceptional root systems |
| Authors: | Yoshinaga, Masahiko Browse this author |
| Keywords: | Hyperplane arrangements | | Linial arrangements | | Characteristic polynomials |
| Issue Date: | Jul-2018 |
| Publisher: | Elsevier |
| Journal Title: | Journal of combinatorial theory. Series A |
| Volume: | 157 |
| Start Page: | 267 |
| End Page: | 286 |
| Publisher DOI: | 10.1016/j.jcta.2018.02.011 |
| Abstract: | 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. |
| Rights: | © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/79003 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 吉永 正彦
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