Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs

Abstract

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.

11 pages, comments are welcome!

References in corpus (4)

• The freeness of ideal subarrangements of Weyl arrangements
• Signed graphs and the freeness of the Weyl subarrangements of type $B_{\ell }$
• Eulerian polynomials for subarrangements of Weyl arrangements
• Worpitzky partitions for root systems and characteristic quasi-polynomials

Cited by in corpus (1)

• Period collapse in characteristic quasi-polynomials of hyperplane arrangements