Incidences, Tilings, and Fields
Abstract
Abstract The master theorem, introduced by Richter-Gebert and generalized by Fomin and the first author, provides a method for proving incidence theorems of projective geometry using triangular tilings of surfaces. We investigate which incidence theorems over ${\mathbb{C}}$ and ${\mathbb{R}}$ can or cannot be proved via the master theorem. For this, we formalize the notion of a tiling proof. We introduce a hierarchy of classes of theorems based on the underlying topological spaces. A key tool is considering the same theorems over finite fields.
Fields of Study & Subjects
Quasicrystal Structures and Properties
Advanced Combinatorial Mathematics
Finite Group Theory Research
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 7
- Publication date
- 1 April 2026
- Language
- EN