Characteristic quasi-polynomials of deletions of Shi arrangements of type B and their period collapse

Akihiro Higashitani; Norihiro Nakashima

Paper

Characteristic quasi-polynomials of deletions of Shi arrangements of type B and their period collapse

Abstract

Characteristic quasi-polynomials are the enumerative functions counting the number of elements in the complement of hyperplane arrangements modulo positive integers.In this paper, we compute the characteristic quasi-polynomials of the restriction of the Shi arrangement of type B by one given hyperplane. As a corollary, we determine whether period collapse occurs in the characteristic quasi-polynomial of the deletion of the Shi arrangement of type B. This implies the solution for the conjecture posed by Higashitani, Tran and Yoshinaga in the case of the Shi arrangement of type B.