Free paths of arrangements of hyperplanes
Abstract
In this paper, we study the free path problem, i.e. if we are given two free arrangements of hyperplanes, then we can connect them by free arrangements or not. We prove that if an arrangement [Formula: see text] and [Formula: see text] are free, then at least one of two among them is free. When [Formula: see text] is in the three-dimensional arrangement, we show a stronger statement.
Fields of Study & Subjects
Mathematics and Applications
Point processes and geometric inequalities
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- International Journal of Mathematics
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 37
- Issue
- 11
- Publication date
- 3 June 2026
- Language
- EN