Combinatorial Aspects of Mixed Arrangements

Abstract

In this paper, we consider mixed arrangements, which are composed of
hyperplanes (or subspaces) and spheres. We investigate the posets of
their intersection sets and calculate the Möbius functions of the
mixed arrangements through the hyperplane (or subspace) arrangements’
Möbius functions. Furthermore, by employing the method of deletion
and restriction, we derive recursive formulas for the triples of
these mixed arrangements.