Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs
| Autor: | Tran, Tan Nhat, Tsuchiya, Akiyoshi |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Comptes Rendus. Math\'ematique 359 (2021), 665--674 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.5802/crmath.210 |
| Popis: | The class of Worpitzky-compatible subarrangements of a Weyl arrangement together with an associated Eulerian polynomial was recently introduced by Ashraf, Yoshinaga and the first author, which brings the characteristic and Ehrhart quasi-polynomials into one formula. The subarrangements of the braid arrangement, the Weyl arrangement of type $A$, are known as the graphic arrangements. We prove that the Worpitzky-compatible graphic arrangements are characterized by cocomparability graphs. Our main result yields new formulas for the chromatic and graphic Eulerian polynomials of cocomparability graphs. Comment: 11 pages, comments are welcome! |
| Databáze: | arXiv |
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