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

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 complete solution for the conjecture posed by Higashtiani, Tran and Yoshinaga.