Characteristic quasi-polynomials for deformations of Coxeter arrangements of types A, B, C, and D

Abstract

Kamiya, Takemura, and Terao introduced a characteristic quasi-polynomial which enumerates the numbers of elements in the complement of hyperplane arrangements modulo positive integers. In this paper, we compute the characteristic quasi-polynomials for specific arrangements which contain the Coxeter arrangements of types A, B, C, and D described by the orthonormal basis. We also compute the characteristic quasi-polynomials for their deletion arrangements and we can show that they are factorized. From this result, the poset generated by hypertori of the corresponding toric arrangement is an inductive poset.