Hyperplane arrangements between Shi and Ish

Abstract

We introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions -- the connected components of the complement of the union of the hyperplanes -- which can be bijectively labeled with the Pak-Stanley labelling. In addition, we characterise the Pak-Stanley labels of the regions of this family of hyperplane arrangements.