Eulerian polynomials for subarrangements of Weyl arrangements

摘要: Let $\mathcal{A}$ be a Weyl arrangement. We introduce and study the notion of $\mathcal{A}$-Eulerian polynomial producing an Eulerian-like for any subarrangement $\mathcal{A}$. This together with shift operator describe how characteristic quasi-polynomial new class arrangements containing ideal subarrangements can expressed in terms Ehrhart fundamental alcove. The method also extended to define two types deformed families Shi, Catalan, Linial compute their quasi-polynomials. obtain several known results literature as specializations, including formula via theory due Athanasiadis (1996), Blass-Sagan (1998), Suter (1998) Kamiya-Takemura-Terao (2010); relating number coweight lattice points parallelepiped Lam-Postnikov Eulerian third author.